Analyses 7X64  Main Challenge

Our Finest Gifts We Bring

Scores  by Richard Pavlicek

Pa-rum pum pum pum

During the month of December, 2003, these six problems were published on the Internet as a defensive-play contest. In each case your opponents had offered you a “gift” by overbidding, and your goal as East was to choose the best defense to collect it from the choices offered. All bridge players were invited to participate.

Problem 1

2

3

4

5

6

Final Notes

Leif-Erik Stabell Wins Again!

The scoring average was up this month — the highest ever for any defensive-play contest (not counting the one on opening leads). The consensus zeroed in on two of the best answers, and narrowly missed a third. I’d like to say this was because I was generous at Christmastime, but I tried to be as devious as ever.

If you people start getting too smart, I may have to throw in a seventh choice: None of the above.
Boy, did I hate that on school exams.

In the overall standings, Zahary Zahariev held his lead with an impressive 59.00 average over Charles Blair (Urbana, Illinois US) with 58.75. Next with 58.00 are John Reardon and Leif-Erik Stabell (surprise, surprise) followed by Carsten Kofoed (Sweden) and Rob Stevens (Santa Cruz, California US), each with 57.50.

In the December Bot’s Eye View, Jack came through with an impressive 55 (best bot score ever in a play contest) easily topping the pack and increasing its overall lead as well. Bridge Baron was a distant second with 46. Will GIB ever make a comeback?

Since I began this activity in September of 2000, there have been 40 monthly events (20 bidding polls and 20 play contests) with a total of 26,063 entries, comprising 4195 persons from 86 countries. A new country was added this month: Welcome to Bela Russ of Guatemala (GT). And while I’m looking back, a special thanks to the only four persons who have entered all 40 events: Charles Blair, Bill Cubley, Josh Sinnett (all US) and Meelis Tiitson (Estonia).

Bidding is standard (except as noted) and you use standard leads and signals.
For a reference see Standard American Bridge. Assume all players are experts.

Each problem offered six plausible lead options. The merit of each is scored on a 1-to-10 scale based on my judgment, which may be influenced by comments received.

Problem 1

Matchpoints	K 9 8 7 3		West	North	East	South
None vul	4		Partner	Dummy	You	Declarer
	9 6 5 4 3					1 NT
	10 3		Pass	2 1	Dbl	3
		A 4 2	Pass	4	Pass	Pass
Lead: 2		A K 7 6 5	Pass
		Q
4 South		A J 9 7	1. Jacoby transfer

Trick	Lead	2nd	3rd	4th
1. W	2	4	A	9

Your Next Lead	Award	Votes	Percent
A	10	83	10
J	8	129	15
Q	7	293	34
2	6	254	30
6	3	83	10
K	1	12	1

There’s nothing shy about the opponents’ bidding, and after seeing dummy you have some regrets about not doubling again. Four spades has all the appearance of a save against a makable 4 your way; but that’s water under the bridge. Your only concern now is to beat the contract. If partner has a diamond trick (or remotely the K) this will be easy, but all you can be sure of are three tricks.

The instinctive defense is to shift to your singleton diamond — not so much to get a ruff from partner (who probably has no entry) but to remove declarer’s transportation in that suit, perhaps forcing declarer to surrender the ruff. Not so fast. The danger is that South may have a pat diamond holding (AKJ) and be able to draw three rounds of trumps then establish the long diamond in dummy. Consider this layout:

Matchpoints	K 9 8 7 3		Trick	Lead	2nd	3rd	4th
None vul	4		1. W	2	4	A	9
	9 6 5 4 3		2. E	A!	5	4	3
	10 3		3. E	J	K	2	10
5		A 4 2	4. S	6	8	7	7
10 8 3 2		A K 7 6 5		continued below…
10 8 7 2		Q
Q 8 4 2		A J 9 7
	Q J 10 6
	Q J 9
	A K J
4 South	K 6 5

Declarer will win the diamond and lead trumps, after which you cannot tap dummy (without setting up the Q); then declarer will romp home with 10 easy tricks. It is imperative to set up a tap on dummy without giving declarer an extra winner. Note that a heart return* will not suffice, as declarer will win the Q and eventually ruff all his losers to complete a dummy reversal.

*If South held Q-10-9, the 6 return might work (declarer is likely to finesse the 10); but this is a poor gamble. Restricted choice favors Q-J-9 (with Q-10-9 declarer might have played the 10), plus there’s no real need to take such a risk.

“I am a poor boy too, pa-rum pum pum pum.”

You must return a club, and specifically the ace first — else declarer will win the K and lead the Q for a loser-on-loser play. After winning the K, declarer will probably ruff a club with the 7 to reach this position with the lead in dummy:

win 2	K 9 8 3		Trick	Lead	2nd	3rd	4th
	—		5. N	3	A!	6	5
	9 6 5 4 3		6. E	Q	A	2	3
	—		7. S	Q	3	8	5
5		A 4 2	8. N	9	2	10	8
10 8 3		K 7 6 5	9. S	J	10	K	6
10 8 7 2		Q	10. N	4	4!	J	7
Q		9		Declarer fails
	Q J 10 6
	Q J
	A K J
North leads	—

Next comes the 3. Careful! You must hop and return a spade or a diamond, which leaves declarer with insoluble transportation problems. If you carelessly duck, declarer will win in hand; ruff a heart; diamond to king; ruff a heart and lead a trump, leaving South high.

The recommended defense ( A then J) is a clear winner, as it also works if South has Q-J-10-x Q-10-9 A-K K-Q-x-x (as would other defenses). If South has Q-J-10-x J-10-9 A-K-J K-Q-x, nothing works — declarer can always ruff two hearts in dummy and lead toward clubs (if you haven’t) to establish his hand.

Of the non-club leads, the Q and 2 are next best, having about equal chances. The edge goes to the Q because it’s more likely to produce a two-trick set. Either heart lead is poor, though the 6 is better than the K because declarer might misguess. Note that a heart return gives declarer the tempo for a dummy reversal with Q-J-10-x J-9-8 A-K K-Q-x-x, while any other defense sets the contract.

Comments for the A

Leif-Erik Stabell: The only defense against Q-J-x-x Q-J-9 A-K-J K-x-x, quite a likely layout.

Dean Pokorny: When declarer holds Q-J-10-x Q-J-10-9 A-K-J K-x, the only way to beat 4 is to force him with clubs. After A and another club, I take the A and shoot back another club. This is the only way to break the declarer’s control of the board; he has no winning play.

Zahary Zahariev: Nothing to do against Q-J-x-x ?-?-9 A-K-J-x K-x, and no need to worry if South has Q-J-x-x Q-x-x A-K K-Q-x-x, or if partner has a diamond trick. The interesting South hand is Q-J-x-x Q-J-9 A-K-J K-x-x, and I must return ace and another club to remove a trump entry in dummy before declarer can clear trumps and unblock diamonds.

Manuel Paulo: … If South has a hand like Q-J-10-x J-10-9 A-K-J K-Q-x, or Q-J-10-x Q-J-9 A-K-J-x K-x, I have no good return; against Q-J-10-x Q-10-9 A-K K-Q-x-x, I can lead any card but a heart or a low club; against Q-10-x-x Q-J-10-9 A-K K-Q-x, I can lead any spade, the Q or A; and against Q-J-10-x Q-J-10-9 A-K-J K-x, or Q-J-10-x Q-J-9 A-K-J K-x-x, I must lead the A and a club. Starting with the J doesn’t work because South can win and lead a heart honor to pitch dummy’s club.

John Reardon: South may have Q-J-10-x Q-J-x A-K-J K-x-x, in which case the J loses. South lacks the entries to ruff his three losers without giving me a diamond ruff.

Imre Csiszar: In the critical case when South holds A-K-J, dummy must be forced to ruff before the fifth diamond is set up. If West encourages, dummy will be shortened in clubs; otherwise in hearts.

Tim DeLaney: I will lead two rounds of clubs, then a third when I win the A to force dummy to use an entry prematurely. This makes it impossible to establish and cash dummy’s diamonds if declarer has something like Q-J-x-x Q-J-9 A-K-J K-x-x.

Charles Blair: Preparing to give South a ruff-and-discard.

David Grainger: If partner has a diamond trick, it isn’t going anywhere; but if he has 10-x-x-x, I need to tap the table. The  A should let me decide which round-suit queen [partner has].

Lajos Linczmayer: If South has Q-J-10-x Q-J-9 A-K-J K-x-x, or Q-J-10-x Q-J-9-8 A-K-J K-x, the lead of A, J and a later third round makes it impossible for South to establish diamonds.

Weidong Yang: The only chance for declarer is to set up the diamond suit. If he has A-K-J, I must try to shorten dummy’s trumps, which are important to set up and cash diamonds. A club return is necessary, and I hope partner has the Q. Furthermore, I should cash the A in case declarer has Q-J-9 originally, else he could discard dummy’s remaining club on the Q…

Neil Morgenstern: What if declarer’s diamond holding is exactly A-K-J? I want to attack clubs at every opportunity, as this is the best chance to prevent him from setting up the diamonds. The  A is better than leading the jack first in case [declarer has Q-J].

Gabriel Nita-Saguna: … If declarer has A-K-J K-Q-x, there is nothing I can do to prevent 10 tricks. If he has A-K-J K-x-x, I’ll have to tap dummy in case he tries to draw trumps. If, however, he has A-K K-Q-x-x, I should remove the entries to his hand to prevent a dummy reversal. Cashing the A, followed by the jack, will not only remove an entry but allow partner to signal if he has the Q…

Rolf Mattsson: I must force dummy to take an early club ruff in case declarer has A-K-J and partner the Q. I do not play the J in case declarer has Q-J. If partner has the K or a diamond trick, declarer will always go down.

Malcolm Ewashkiw: Playing declarer to have something like Q-J-x-x Q-J-9 D A-K-J K-x-x, and hoping for an [eventual] table lock to score one of my small trumps.

Amiram Millet: Crucial when South holds Q-J-x-x Q-J-9 A-K-J K-x-x.

Chris Willenken: At some point, I may have to tap dummy to stop declarer from drawing trumps and ruffing diamonds good if he holds A-K-J. So I shift to the A to find out which rounded suit to use to tap dummy. A lower club risks finding declarer with Q-J-10-x Q-J-10-9 A-K K-x-x, where he now succeeds with a loser-on-loser play.

Stop press! I was running short of comments and wish to thank these two celebrities who graciously agreed to fill in. Also leading the A:

George W. Bush: This has a better chance to cash than the K. The only alternature is to try a nukular defense with the Q; but if it wins, I wouldn’t have any more diamonds to play with. You didn’t say who my opponents were; but if Colon Powell is South, I would have doubled. No way would he make 4 — he likes his job.

Arnold Schwarzenegger: Then the J. You can believe me now or believe me later, I’ll be back with more clubs. I promise you, I will pump this declarer — just like I pumped up Sacramento and will pump you up. When this hand is over, declarer will wish he never crossed paths with the Pumpenator.

Problem 2

Matchpoints	Q 2		West	North	East	South
Both vul	K J 9		Partner	Dummy	You	Declarer
	A K 9 5 4 3			2	Pass	2
	A K		Pass	3	Pass	3
		A K 8 3	Pass	4	Pass	Pass
Lead: 4		A 4	Pass
		Q 2
4 South		Q 8 7 6 3

Trick	Lead	2nd	3rd	4th
1. W	4	Q	K	6

Your Next Lead	Award	Votes	Percent
A	10	451	53
4	9	48	6
6	6	246	29
A	5	48	6
2	4	24	3
Q	2	37	4

Amazing. North has about as much of a 2 opening as you do, yet they coast into a game that might easily make with the friendly breaks if South has Q-10-x-x-x and out. This problem is derived from an actual deal on which I was East:

Matchpoints	Q 2		Trick	Lead	2nd	3rd	4th
Both vul	K J 9		1. W	4	Q	K	6
	A K 9 5 4 3		2. E	4!	5	3	K
	A K		3. N	A	3	5	2
J 7 5 4		A K 8 3	4. N	K	6	10	4
7 3 2		A 4	5. N	2	A	9	5
J 10		Q 2	6. E	A!	6	2	9
J 9 4 2		Q 8 7 6 3	7. E	3	10	J	J
	10 9 6		8. N	A	2	6	10
	Q 10 8 6 5		9. N	K	Q	7	J
	8 7 6		10. N	3	7	8	7
4 South	10 5			Declarer fails

In real life North opened 2 NT, and South transferred to 3 , which was passed out — a bit more reasonable than the Fantasy Land 2 . I led the A (playing ace from A-K) and continued the suit after partner’s seven, North ruffing the third round with the 9. Next came the K to my ace, and declarer had 10 easy tricks. If I ducked the K, declarer must cash his minor-suit tops before leading a second heart.

Afterwards I noticed I could have held it to three with a low-heart at trick two. No matter what declarer does, he can later be forced to ruff the third spade after two hearts are led, then West must score his remaining trump with a diamond ruff. This defense seemed far-fetched from my perspective, but if the contract is played from the South side it seems quite reasonable if not indicated — hence my contrived auction to create this problem. I expected to give the top award to the 4.

“Come, they told me, pa-rum pum pum pum.”

Alas, things don’t always go as planned. Additional study, combined with the input of many excellent comments, opened my eyes to many other possible layouts. On the given auction, there is no real indication that South has the Q (or any points for that matter since 3 is forcing) so the deal could just as easily be:

Matchpoints	Q 2		Trick	Lead	2nd	3rd	4th
Both vul	K J 9		1. W	4	Q	K	6
	A K 9 5 4 3		2. E	4?	10!	2	9
	A K		3. S	3	7	J	A
9 7 5 4		A K 8 3		Declarer succeeds
Q 7 2		A 4
J 10		Q 2
J 9 4 2		Q 8 7 6 3
	J 10 6
	10 8 6 5 3
	8 7 6
4 South	10 5

If East now shifts to the 4, it simply gives away the contract (South puts up the 10 to avoid a guess). In fact the 4 is so bad that if East cashes the A, he could lead any other card in his hand and beat the contract. Note that giving South an entry with the J doesn’t matter because East can win the first heart and lock declarer in dummy.

Declarer’s play of the Q from dummy is consistent with either example. South must either hold J-10 or lack the J altogether; i.e., he would not play the queen with J-x-x. Also note that declarer would always play the queen with J-10-x (to leave rope for East to make a fatal underlead) but might not bother with a worthless holding*, which adds weight to the second example.

*This reminds me of the time I went down in a cold 5 (reached after a slam try). My only losers were clubs, with Q-x in dummy opposite x-x. A club was led to RHO’s 10, and the diamond return was ruffed. LHO had underled his A-K-J. Argh! When we compared scores with Kaplan and Kay, I was surprised to see minus 50 a push. Norman then said something like, “They bid the slam, too.” It wasn’t clear whether I should have fessed up, but I did. After a brief pause in amazement, Edgar offered with his usual dry wit, “Yes, it’s encouraging that our teammates at least know how to bid.”

There are other cases where the low heart return costs, for example:

Matchpoints	Q 2		Trick	Lead	2nd	3rd	4th
Both vul	K J 9		1. W	4	Q	K	6
	A K 9 5 4 3		2. E	4?	3	2	9
	A K		3. N	K	A	5	7
J 7 5 4		A K 8 3	4. E	A	9	5	2
10 7 2		A 4	5. E	3	10	J	J
J 10 8 6		Q 2	6. N	A	2	7	6
4 2		Q 8 7 6 3	7. N	3	Q	6	8
	10 9 6		8. S	Q	10	4	3
	Q 8 6 5 3		9. S	5	2	A	6
	7		10. N	K	8	9	10
4 South	J 10 9 5		11. N	5	7	8	J

On a heart shift, declarer can simply win and continue hearts; then diamonds can be established no matter what you do next. In contrast, three rounds of spades defeats the contract. When hearts are led, East ducks the first round; then South can be forced in spades, leaving too few trumps to establish diamonds. If declarer instead tries to crossruff, this also fails.

With no clear answer so far (and other significant layouts, too) the best way to get a handle on this was to run a simulation. So I created 1000 random deals, giving South five hearts, exactly three spades* (consistent with the lead and the Q play) and 1-3 diamonds. (If South were void in diamonds, West would have led his singleton club; if South had four diamonds, West would have led his singleton diamond; and five diamonds is too far-fetched with South never raising partner.) Results showed the A and a spade continuation to be superior (by 31 deals) over the 4, which took second place by an even wider margin.

*I did not allow for the possibility that West might have led from three spades (e.g., J-x-x) as this seemed unlikely (West would usually have 4+ clubs and prefer a club lead). Further, whatever small impact it had would favor a spade return, which won anyway.

Curiously, the A came in third in my simulation (narrowly edging out the 6) but this is clearly biased because East gets the next stroke at double-dummy; whereas a club return gives up the lead. Therefore, the 6 deserves third place. Both diamond leads fared poorly (no real surprise), though I upgraded the 2 since declarer might misplay the suit with 10-x-x or J-x-x.

Comments for the A

Leif-Erik Stabell: Hoping that South is no better than 10-x-x Q-8-6-x-x x J-x-x-x. Three rounds of spades and accurate defense thereafter should eventually promote the 10.

Dean Pokorny: If declarer has a weak hand like J-9-x-x 8-7-x-x-x J-x x-x, the only way to beat this is to cash A-K and exit passively [with a club] hoping to make two trump tricks. If declarer then plays: A-K, A-K and a diamond, I must ruff with the A…

John Reardon: A hand that matters is something like 10-x-x 10-8-x-x-x J J-x-x-x, when three rounds of spades are essential. This will also defeat a hand like J-10-x 10-8-x-x-x x-x-x x-x. …

Bruce Neill: If declarer has weak hearts and short diamonds, say, 10-x-x Q-7-x-x-x x J-10-x-x, I may be able to beat him by forcing him to ruff twice. If he ruffs twice in dummy partner’s 10 will be promoted; and if he ruffs once in each hand, he won’t have enough trumps to set up dummy’s diamonds.

Tim DeLaney: Somehow, I must get a trump trick for partner to beat the contract. The play of the Q at trick one seems to indicate South has J-10. If he plays either of these, I will play a club… otherwise, I play a spade to partner’s jack [to tap dummy].

Carsten Kofoed: I hope partner has 10-x-x and 10-x-x-x, so I play spades on every lead I have.

Rob Stevens: Looks as though best chance is to endplay dummy by removing its exit cards and exiting with a club. Hope to find declarer with three diamonds, and hearts headed by the 10.

Sylvain Brethes: … Declarer will be in trouble if partner has the J and 10 (at least 10-7-x), giving South 10-x-x Q-8-x-x-x x J-x-x-x. …

N. Scott Cardell: My plan is to force the board in spades, then we [may] defeat this if partner’s trumps are as good as 10-x-x. …

Weidong Yang: The diamond suit can be set up easily, so my only hope is another trump trick. In some situations, even 10-x-x in partner’s hand will be enough. I continue with the strongest suit we have and never worry about a ruff and discard.

Herbert Bruch: Set up a possible spade ruff if West has J-x-x x-x-x x-x x-x-x-x-x. Also, I must duck the A when declarer pulls trumps.

Barry Rigal: Planning to lock declarer in dummy and let him try to escape with J-10-x 10-x-x-x-x J-x-x Q-x.

Sneha Sridhar: The diamond suit is menacing, and this hand does not look like a gift. In most distributions declarer looks cold to make the contract; but the A and another spade might promote partner’s 10 by forcing dummy to ruff.

Nick Krnjevic: My best chance is to play partner for either 10-x-x or Q-x-x. … Playing three rounds of spades [may] dummy-lock declarer…

Gabriel Ip: Partner seems to have led from J-x-x-x. Punch the dummy and play partner to have 10-x-x.

David Rock: If South has the J, there is no useful discard. Then lead the 6…

Sebastien Louveaux: I must focus on declarer’s x-x-x Q-x-x-x-x x x-x-x-x, which is [one] distribution where my play changes anything. Declarer must establish diamonds and needs two ruffs. I force dummy in spades; duck the first heart; then force declarer with my last spade to promote partner’s 10. …

Julian Pottage: I must keep playing spades if South is 3=5=1=4 with the Q but not the 10.

Sven Pride: Our fourth trick seems like it needs to come from the trump suit, so I’ll try to make dummy ruff…

Dale Freeman: If partner has two diamonds and 10-x-x, declarer will have a problem getting off dummy.

Frances Hinden: I need to generate a trump trick from somewhere. If partner has the J, I will continue spades at trick three; otherwise, play a club next.

Frances brings up the subtle point that partner can tell you whether he has the J by his second-round play. If he plays a low card, you should assume he has the jack. With a holding like 9-x-x-x, he should play the nine. Similarly, with 10-x-x-x (albeit unlikely from declarer’s queen play) he should play the 10.

Albert Ohana: Followed by a third spade… I will take the A on the second round and play a fourth spade, hoping for the best.

Bob Boudreau: Hopefully, I can force dummy to ruff the third spade… If partner has 10-x-x and only two diamonds, declarer will have communication problems.

Hans Holme: [Best] chance is to lock declarer in dummy and hope partner has three trumps. …

Al Goldspiel: Partner may hold J-x-x x-x-x J-x-x x-x-x-x.

David Stern: Looks like we need a second trump trick to beat this so I will keep playing spades, hoping partner has Q-x-x or 10-x-x and it becomes a trick.

Norm Gordon: Then a third spade. My only hope of setting this is to promote a heart trick for partner…

Bogdan Mitran: I hope South holds three diamonds and at most six hearts without the queen — or something like x-x-x-x Q-x-x-x-x x-x x-x (without the 10 and J).

Douglas Dunn: Playing out spades may promote a trump trick for partner if he started with J-x-x and 10-x-x.

Comments for the 4

Zahary Zahariev: … It looks like partner started with J-x-x-x. I hope to find South with 10-x-x Q-10-x-x-x J-x-x x-x. Later I win the A and A, then force dummy to ruff a spade for the auto-kill diamond lead.

Imre Csiszar: In the critical case when South has x-x-x Q-x-x-x-x x-x-x x-x, this…will eventually force declarer to lead a third diamond from dummy, allowing West to ruff.

Charles Blair: Later, win the A and make dummy ruff the J.

Lajos Linczmayer: If South has Q-10-x-x-x and a doubleton diamond, the defense is hopeless. If South has 10-7-6 Q-10-8-x-x J-x-x x-x, a diamond ruff will be the setting trick.

John Lusky: Seeking to lock declarer in dummy if he has 10-x-x Q-10-8-x-x J-x-x J-x or the like. I will win a second trump and play two more rounds of spades (or win a second spade and play A and a third spade).

Julian Wightwick: There are various ways this might go off. Partner could have Q-x-x, or any four trumps. Failing that, if declarer has short diamonds he is in good shape, either by a crossruff or setting up diamonds. So I shall play declarer for 3=5=3=2 shape and make dummy give partner a diamond ruff. If declarer plays a major suit now, I cash the other ace and force dummy. Playing spades immediately doesn’t work because declarer can cash the minor A-Ks before drawing trumps (dentist’s coup).

Sid Ismail: If partner has the J and a doubleton diamond at most, we are beating this for sure. Force dummy after the A. Partner needs only J-x-x-x x-x-x x-x x-x-x-x.

Gabriel Nita-Saguna: … I will play declarer for x-x-x Q-10-x-x-x J-x-x x-x. Later, after winning the A, I will continue with two rounds of spades, locking declarer in dummy; he will have to concede a diamond ruff to partner.

Malcolm Ewashkiw: … If declarer has six hearts, I don’t think we have a chance; so I’ll play partner for three hearts, two diamonds and the J. When I win the A, I’ll play spade, spade to table-lock declarer.

Jing Liu: … When declarer’s shape is 3=5=3=2 [without the J], the 4 will kill him. Later, I can win the A, A and lead another spade to lock declarer in dummy.

Rainer Herrmann: Planning to lock South in dummy should he have three diamonds.

Problem 3

Matchpoints	K 6 5		West	North	East	South
E-W vul	A 10 9		Partner	Dummy	You	Declarer
	K 8 6 5 4 2					1
	K		Pass	2	Pass	2
		Q	Pass	3	Pass	4
Lead: J		Q J 8 2	Pass	4	Pass	5
		Q 10 9 7 3	Pass	6	All Pass
6 South		A Q 9

Trick	Lead	2nd	3rd	4th
1. W	J	2	3	A
2. S	8	2	K	A

Your Next Lead	Award	Votes	Percent
Q	10	70	8
J	9	71	8
Q	6	466	55
Q	5	200	23
Q	3	40	5
2	1	7	1

Your opponents are like the Energizer Bunny — they keep going and going; you almost wonder why they didn’t bid seven. Partner led his singleton hoping for a ruff, so the obvious move is a diamond* return. This might promote a trump trick if partner’s spades are 10-x-x, or it might catch declarer off guard. The latter is mostly a dream, however, as partner’s choice to lead a diamond suggests a singleton.

*Which diamond makes little difference, though the 10 is a poor choice because it marks the jack as shortness. The queen must be right for two reasons: (1) because it’s the card you are known to hold, assuming the jack is honest, and (2) for suit preference, as you want a heart return.

Before doing something impulsive, let’s count declarer’s tricks. Partner’s 2 shows an odd number of clubs, which must be seven on the bidding. This marks South with 6=4=1=2 shape, so he can win six spades (else he’s down no matter what you do), two hearts, two diamonds and one club ruff. That’s 11 tricks, and the layout should be something like this:

Matchpoints	K 6 5		Trick	Lead	2nd	3rd	4th
E-W vul	A 10 9		1. W	J	2	3	A
	K 8 6 5 4 2		2. S	8	2	K	A
	K		3. E	Q?	J	3	4
9 3 2		Q	4. S	7	4	5	9
4 3		Q J 8 2	5. N	K	Q	4	2
J		Q 10 9 7 3	6. N	6	Q	A	3
J 10 6 5 4 3 2		A Q 9	7. S	10	9	5	7
	A J 10 8 7 4		8. S	8	5	6	2
	K 7 6 5			continued below…
	A
6 South	8 7

If you return a diamond, declarer will surely ruff with the J, then ruff a club in dummy. Establishing diamonds is futile with West’s 9 lurking, so there’s nothing else to do but run trumps to reach:

win 5	—		Trick	Lead	2nd	3rd	4th
	A 10 9		9. S	7!	6	9	?
	K 8			East is squeezed
	—
—		—
4 3		Q J 8
—		10 9
J 10 6		—
	7
	K 7 6 5
	—
South leads	—

Ouch! When the last trump is led, dummy pitches a heart, and you are squeezed in the red suits for declarer’s 12th trick.

“So, to honor Him, pa-rum pum pum pum.”

To break up the squeeze, you must return a heart honor. On the surface this does not seem to gain because it sacrifices a heart trick in the process. Not really. If declarer tries to benefit by winning the A, he cannot score a club ruff and the K because dummy lacks an entry after trumps are drawn. If declarer wins the heart in hand, the squeeze is gone.

In theory, it makes no difference whether you lead the Q or J; but I am awarding the top score to the queen* for two reasons: (1) It is psychologically better as declarer will deduce you’re more likely to lead a singleton queen than a jack (or even Q-x versus J-x), hence the jack more strongly implies Q-J, and (2) with all four queens offered as options, it seems only fitting that one of them should win.

*My policy is to break all ties, however slight. Only once in the past did I award dual top awards (August 2002, Problem 2) but that was due to an ambiguous phrase in my presentation, which left two possible interpretations for the correct answer.

Actually, I felt a little sneaky in presenting this problem, as some people may have rejected the Q or J because, if either were correct, I wouldn’t have listed the other. Sorry, if I gotcha. Perhaps you should have reasoned that I wouldn’t have burned two answers to give you a 1-in-4 shot — even for Christmas.

Of the also-rans, the popular Q gets third place, but I couldn’t justify a higher award than 6 because it is much inferior to the top choice. The  Q is effectively the same in practice, though it does offer declarer a double-dummy make with A-J-x-x-x-x (yes, those x’s are small) K-x-x-x A J-8. If you don’t see it, think repeating triple squeeze, with the J as a threat.

Leading the Q is worse, as it solves declarer’s transportation problem to obtain the ruff, simplifying the red-suit squeeze. Last and surely least is the 2. I suppose there’s a chance declarer will hop with the king to preserve dummy’s entry, but it’s still foolish when either honor does the job without risk.

Comments for the Q

Leif-Erik Stabell: I can’t really see the difference in playing the jack, but I have to give up a heart trick in order to avoid a squeeze if South has A-J-10-x-x-x K-x-x-x A x-x — or even more spectacularly, A-J-10-9-x K-x-x-x A J-x-x, where I will be squeezed in three suits with any other return.

Zahary Zahariev: … If South has A-J-10-9-x-x K-x-x-x A J-x, he has 11 tricks and a [working] squeeze in hearts and diamonds. To prevent it, I must return a heart honor. This is not a gift, as there is no way to ruff a club, cash the K and finesse hearts. But queen or jack? They are absolutely equal. Two top answers? What can I do?

Manuel Paulo: If South has A-J-10-9-x-x K-x-x-x A J-8, or A-J-10-9-x K-x-x-x A J-10-8, there is an impending squeeze against me. I lead a heart quack (I can’t see any good reason which to choose) to destroy the twin-entry menace.

John Reardon: I hope you won’t differentiate between which heart honor is played because either is effective when South has a hand like A-J-10-9-x-x K-x-x-x A x-x.

Bruce Neill: Partner’s low club suggests declarer has two clubs. Give him A-J-10-9-8-7 K-7-6-5 A J-8 (as good as he can be), and only a high heart lead now will beat the contract. It gives declarer three easy heart tricks, but only at the expense of giving up either the K or a club ruff — and it breaks up the looming heart-diamond squeeze.

Rob Stevens: At first sight this looks suicidal, but it is essential to break up the squeeze when South has a 6=4=1=2 pattern. If declarer wins in dummy, he cannot both ruff a club and cash the K; and if he wins in hand, the latent squeeze is destroyed.

Sylvain Brethes: I hate to be squeezed, and I may suffer one here, as I think declarer has A-J-10-x-x-x K-x-x-x A x-x. He will not survive if I play the Q (not sure of the difference between the queen and jack, though).

David Grainger: Partner only has three red cards… and this will either knock out the A (then declarer will never be able to ditch his fourth heart) or declarer will win the K and no longer be able to execute a squeeze. … As for which heart honor to lead, declarer will probably be expecting the jack if I have both. :)

Lajos Linczmayer: South’s hand cannot be better than A-J-10-9-8-7 K-7-6-5 A J-8. In this case, only the Q or J defeats the contract. If I lead the Q, declarer is [more likely] to misguess hearts because [it is plausible] to lead an unsupported queen; but an unsupported jack would be fatal if West held the king.

N. Scott Cardell: I don’t see why both the Q and J are listed…as either one should defeat declarer, who must be 6=4=1=2 (or 5=4=1=3 in a hopeless contract). … Declarer probably will win in hand to preserve a late entry to the diamonds; but he is an entry short with the 5-1 break, and partner may get an overruff. Even if declarer wins in dummy and runs the 10, I just duck; then he can’t both ruff his club loser and score the K… Whichever hand he wins in, his entries for a red-suit squeeze are destroyed. …

Julian Wightwick: Declarer seems to be 6=4=1=2 shape, so I need to break up the red-suit squeeze. If he guesses hearts, it won’t matter because he can’t arrange to ruff a club, draw trumps and cash the K. … I’ll lead the queen just because many players tend to lead the jack in this situation.

Weidong Yang: I see no difference between the Q and J, so these options would quickly be discarded in a loose contest. However, I think declarer’s hand is something like A-J-10-9-8-2 K-7-5-4 A 10-8. I will be squeezed soon, so the only defense is attack dummy’s entry. Thanks to partner’s trumps, declarer cannot ruff a club, finesse hearts and cash the K. I choose the Q since it is unnecessary to disguise the layout. …

Sid Ismail: Anything else, and I get squeezed in the red suits in the four-card ending. Of course, declarer will ruff a crafty Q with the knave, holding A-J-10-9-8-7 K-x-x-x A 10-8.

Barry Rigal: Trying to break up a red-suit squeeze. … If declarer wins in dummy and passes the 10, he can’t cope when I duck.

Toby Kenney: Disrupt communications for the squeeze… If declarer wins with the ace, he can finesse hearts; but he can’t make both a club ruff and the K.

Gabriel Nita-Saguna: Declarer’s shape seems to be 6=4=1=2. Not returning a heart would result in me getting squeezed in the red suits for 12 tricks. Returning the Q or J will beat the contract, provided I do not cover the next heart from dummy (if declarer wins the ace and continues hearts). My preference goes to the Q, which seems a bit trickier against an expert declarer…

Steve White: I need to attack declarer’s entries for the red-suit squeeze. Declarer cannot ruff a club and enjoy the K if he lets the heart ride to the ace. The  Q and J seem equally good.

Malcolm Ewashkiw: I don’t see any difference between the Q and J. … Declarer should be 6=4=1=2, and the plan is to break up the impending heart-diamond squeeze. Partner’s diamond lead already knocked out the A, breaking up a possible crisscross squeeze.

Yes, Partner had it all figured out from the start, “Better lead the J to kill the old crisscross.”

Julian Pottage: This breaks up a squeeze if South has A-J-10-x-x-x K-x-x-x A x-x.

Frans Buijsen: If South has A-J-10-9-x K-x-x-x A J-x-x, a three-suit squeeze threatens to develop. Playing a high heart now is the only way to break the communication. I can’t see the difference between the queen and jack, so I’ll play the normal card.

Dale Freeman: [To prevent] declarer from squeezing me in the red suits. If he wins the K in hand, there is no squeeze; if he wins the A in dummy, he [cannot] score both a club ruff and the K.

George Klemic: This looks like it gives declarer the heart suit, but the timing is not there to enjoy it. Give declarer the expected 6=4=1=2 (5-5 is possible but then my 8 is a key card). If I play back [anything but a heart honor] I will get squeezed in the red suits. After the A is gone, there is no way back to dummy after drawing trumps…so declarer cannot win the K [if he ruffs a club]. As to whether the queen or jack is better, I figured since four of the choices were queens, odds are one is right. :)

Junaid Said: A heart honor seems best to prevent the impending red-suit squeeze. Assuming declarer will almost always guess the heart position right, I can’t see much difference between the queen and jack. Maybe this should convince me to choose another answer, but that’s what I’d play at the table.

Comments for the J

Dean Pokorny: Returning a high heart prevents a possible progressive squeeze when declarer holds something like A-J-10-9-x K-x-x-x A J-x-x. …

Imre Csiszar: Breaks up the heart-diamond squeeze. If South guesses to win in dummy and finesse against my queen, he will be unable to ruff his club and win the K. The Q would be equally good.

Carsten Kofoed: South has realized his options; no one would lead the J unless singleton or from 5+ cards. Therefore, I’ll start the heart attack by sending an elephant into the china store. I choose the knave because it would not be nice to let a lady do this dirty job. South has A-J-10-9-x-x K-x-x-x A J-x. Even though I give up a heart trick now, I will get it back in the end (or West will ruff the K).

John Lusky: Why lead a queen when I can lead a jack? Seriously, if declarer has the expected A-J-10-9-8-x K-x-x-x A x-x, I can be squeezed in the red suits unless I disrupt declarer’s heart communication. Either the Q or J will do the trick as long as I don’t cover the 10 or nine if led from dummy. Either the K will go to sleep, or declarer won’t get his club ruff — there is no 12th trick.

Herbert Bruch: Break up the diamond-heart squeeze.

Sneha Sridhar: Either heart honor breaks the squeeze against me in hearts and diamonds. …

Neil Morgenstern: I must lead a top heart. It is illusory that this gives away a trick because if I lead, say, a diamond, declarer may be able to ruff high; ruff a club (if he was 6=4=1=2 initially); play off trumps, and ouch! … Either top heart will break this up, but which one? …

Rolf Mattsson: I need to break up the entry for a heart-diamond squeeze. It can hardly matter if I play the Q or J. If declarer wins the A, he will be unable to take a club ruff and cash the K.

David Caprera: Whether I try to break up the squeeze with the Q or J…depends on my opponent. …

Sebastien Louveaux: Only a red-suit squeeze can save declarer, but he needs both heart honors for that purpose. So I must lead a heart honor and, if the ace is won, not cover the 10 if led from dummy (otherwise, dummy will have a late entry to cash the K when partner is out of trumps).

Sven Pride: Breaking up squeeze entries when declarer has A-J-10-9-x-x K-x-x-x A J-x.

Chris Willenken: With a club ruff in dummy, declarer has 11 tricks if he holds the likely A-J-10-x-x-x K-x-x-x A x-x. If I don’t shift to hearts, I’ll be squeezed in the red suits for a 12th trick.

Bob Boudreau: Playing declarer for 6=4=1=2 with all the spots in spades. This avoids being squeezed…

Hans Holme: Tempting to return a diamond, but that would help declarer set up the last diamond if his (six) trumps are solid; or I would suffer from being squeezed. A heart return is the only solution. … Even if declarer reads the heart position (he should, of course) he will be unable to finesse hearts, ruff his remaining club and enjoy the K. No matter which hand wins my jack, I cannot be squeezed.

Jing Liu: I assume declarer’s hand is A-J-10-9-8-7 K-7-6-5 A J-8. To avoid the squeeze in hearts and diamonds, I must return a heart honor. …

Paulino Correa: Declarer is 6=4=1=2 (partner flagged an odd number of clubs), certainly with A-J and probably A-J-10. Eleven tricks are his, and the 12th will come from a heart-diamond squeeze if his A-K are left quiet. … Even if declarer guesses hearts, disrupting his double entry prevents the squeeze; and he’ll be unable to eliminate partner’s three trumps, discard his fourth heart on the K, and ruff his club — down one.

Sim Therrell: This looks crazy, but I…have to break up the squeeze in case South’s spades are solid.

Xiongwen Gu: Declarer should be 6=4=1=2, and this kills the squeeze; the Q also works.

Rainer Herrmann: On Monday, Wednesday and Friday, play the queen; on any other day, the jack looks better. :)

Problem 4

Matchpoints	7 2		West	North	East	South
E-W vul	10 4 2		Partner	Dummy	You	Declarer
	K Q J 10 8 7			1	Dbl	Rdbl
	A 9		1	2	Pass	2 NT
		A Q 6 3	Pass	3 NT	Pass	Pass
Lead: 4		K 8 7 5	Pass
		A 5
3 NT South		Q 7 5

Trick	Lead	2nd	3rd	4th
1. W	4	2	A	5

Your Next Lead	Award	Votes	Percent
8	10	109	13
5	7	146	17
5	6	63	7
Q	5	193	23
Q	4	137	16
3	3	206	24

You seem to have been shafted, as the opponents have reached an aggressive game that is likely to make. Many people won’t even open the North hand 1 (preferring 2 ) let alone continue to game after an invitation. Certainly, you must beat this to score any matchpoints.

The spade layout is clear: South must have the king for his 2 NT bid, so partner must have exactly J-9-8-4. (South cannot have K-J-5, as partner would have led the 10 from 10-9-8-4.) Therefore, a spade return establishes two more tricks; but that’s not enough. Declarer will force out the A and have nine tricks — K, A, A, five diamonds, and either the K or Q (finesse) — while you only have four.

What about killing dummy’s club entry? This certainly might work, but partner probably needs both the K and three diamonds — quite a parlay. Nobody likes long shots. Your chances would be much better if you needed only one favorable holding.

“The ox and lamb kept time, pa-rum pum pum pum.”

Your best chance involves a matter of timing and only requires partner to have the Q (not doubleton). Consider this layout:

Matchpoints	7 2		Trick	Lead	2nd	3rd	4th
E-W vul	10 4 2		1. W	4	2	A	5
	K Q J 10 8 7		2. E	8!	6	Q	2
	A 9		3. W	8!	7	Q	10
J 9 8 4		A Q 6 3	4. E	3	K	9	4
Q 9 3		K 8 7 5	5. S	2	6	K	A
9 6		A 5	6. E	6	3	J	7
J 8 6 2		Q 7 5		Declarer fails
	K 10 5
	A J 6
	4 3 2
3 NT South	K 10 4 3

Declarer will have an easy make after either black-suit return, but not if you shift to a heart. The whipsaw attack forces declarer to duck, else you can win three hearts and two aces; then partner can switch back to spades to establish the setting tricks.

How will partner know to switch? After all, you might have A-10-x-x K-J-x-x A-x Q-x-x, in which case a heart return is necessary. He won’t unless you guide him by leading the 8. When he wins the Q, he can deduce the heart layout* and revert to spades. For this reason, the 5 was demoted considerably in the award scale, as it rates to work only when partner has Q-J-x (and with that holding he might have led the Q originally).

*It is possible, I suppose, that you might shift to the 8 with A-10-x-x A-K-J-8 x-x Q-x-x in case partner held Q-x; but the actual situation is far more likely. In any event, it’s the best you can do.

Second place goes to the 5, which is clearly the better way to attack clubs. If declarer has J-x-x-x with three diamonds, you must be able to cash three clubs upon winning the A, and this is impossible if you begin with the queen. Leading a low club is also better when the club attack is futile because South will almost always put up the king to protect dummy’s entry; hence, leading the queen gives away a trick when South has K-J-x (or longer).

The worst return is a spade, as it offers no real hope to beat the contract. While this ensures no overtricks, such a concern is trivial under the circumstances. The  Q is definitely better than a low spade, as South might take the bait* and duck (then you can switch to hearts), but South should reason that with A-Q-x an expert would play the queen at trick one if he planned to continue spades.

*Note that from South’s point of view the 4 opening lead does not indicate a four-card suit until he sees the 3. Hence, East must conceal that card to have any hope with a spade return.

My award for the 3 may be generous, but it received the most votes, and I’m in a good mood after toasting the New Year with a glass of champagne. Don’t worry! Champagne doesn’t affect me… I’m as judge as a sober!

Comments for the 8

Leif-Erik Stabell: Hoping for J-9-x-x Q-x-x x-x x-x-x-x opposite, and a switch back to spades at trick three. The  5 might work if partner is as good as K-10-8-x; but then he would probably have led one. In any case, South is a big favorite to hold the K or three diamonds, or both.

Dean Pokorny: [Best chance] to beat 3 NT is to get one heart and two more spade tricks before the diamond suit is established. So I return a discouraging heart — making a nice Morton’s Fork Coup. If declarer hops with the A, we have three heart tricks plus two aces; if he ducks, partner takes the Q and returns a spade, giving us three spades, one heart and the A.

Zahary Zahariev: If South has a typical K-10-5 A-J-x x-x-x K-10-x-x, I must find a fifth trick, and the solution is to lead hearts. Declarer can’t hop with the A; then after partner wins the Q, he must go back to spades — so the 8 is better.

Manuel Paulo: South should hold the A and both black kings (partner’s spade suit is J-9-8-4, for certain). If South has A-Q or A-x-x-x, he trots out nine tricks; so I assume West has at least Q-x-x. … After winning the heart trick, partner must switch to spades, so I lead the 8 to help partner. If South goes up with the A to lead diamonds, we can cash three heart tricks and the pointed aces. South’s hand is likely similar to K-10-5 A-J-x x-x-x K-J-x-x.

John Reardon: I hope South has something like K-10-5 A-J-x x-x-x K-10-x-x, so we must set up one heart to go with three spades and a diamond (or one spade, three hearts and a diamond if South takes the A). South should not duck Q if I try that old trick. Partner should realize the 8 is not fourth-best and switch back to spades after winning Q. We will get a terrible result if 3 NT makes; so it is correct to try to defeat it, even at pairs.

Imre Csiszar: Though 3 NT appears to be a fair contract, it will rarely be bid on 22 points or less; so it is justified to risk overtricks to try to beat it. The  8 wins if West holds Q-x-x, with which he will return a spade after winning the Q. …

Bruce Neill: Declarer is marked with K-10-5 (otherwise partner would have led an honor) so I can see three spade tricks and the A. The fifth trick will be in hearts if partner has as little as Q-x-x. Declarer has to duck the first heart to protect his double stopper; then partner can switch back to spades. I’d better lead a high heart spot to tell partner what to do.

Tim DeLaney: Trying to knock out the A is tempting but unlikely to succeed. I am hoping instead that declarer has K-10-5 A-x-x x-x-x K-J-x-x, in which case we must get a heart trick before knocking out the K. I lead the 8 to insure that partner switches back to spades when he wins the Q. This would be necessary if declarer has the J.

Rob Stevens: Hope to find South with K-10-5 A-J-x x-x-x K-x-x-x or similar. Declarer cannot win the A, then partner should switch back to spades.

Sylvain Brethes: Assuming South has a hand like K-10-5 A-J-x-x x-x-x K-x-x, it’s time to play a heart fast!

For sure. You better make that very fast… before declarer comes out of his nap.

John Lusky: The best chance seems to be to play declarer for something like K-10-5 A-J-9 x-x-x K-x-x-x. In that case, I need to steal a heart trick before reverting to spades. I lead the 8 to give partner a good chance to figure out that a shift back to spades may be warranted.

Julian Wightwick: This works if partner has Q-x-x… I lead the 8 (not the five) to encourage partner to switch back to spades at trick three.

Weidong Yang: The normal thinking is to remove the A, dummy’s only entry… but partner has little chance to hold the K… and I expect declarer’s shape to be 3=3=3=4, which means an unbreakable link in diamonds. I must try to seize five tricks before declarer can run diamonds. Hoping partner has the Q, I lead 8 to tell him not to return a heart…

Barry Rigal: Partner may have J-x-x-x Q-x-x x-x 10-x-x-x, so he needs to win the Q and shift back to spades to set the hand. Will he? I doubt it. :)

Sneha Sridhar: No-brainer defense would be to play the Q to remove dummy’s entry to diamonds; but declarer holds the K. A spade return ensures only four tricks for the defense, hence a heart return. … If declarer ducks the heart [with A-J-x], partner must return a spade; hence the 8 instead of the five.

Nick Krnjevic: I assume declarer has something like K-10-5 A-J-x x-x-x K-x-x-x. A spade return is never right since we set up only three spades plus a diamond. … A heart forces declarer to duck, then partner can revert to spades. I must lead the 8 so partner understands [what to do].

Gabriel Nita-Saguna: This is a timing problem. I’ll play partner for holding Q-x-x and J-x-x-x. Declarer can’t afford to jump with the A, as he would lose three hearts, one spade and one diamond. Then, after winning the Q, partner can switch back to spades to establish five winners… Returning the 8 (as opposed to the five) should convey the message to partner…

Rolf Mattsson: Partner will not have the K, and with only J-x-x-x, he will not have Q-x-x-x (since he bid 1 ). A club shift may be good if partner has the K and three diamonds, but the best chance is that partner has Q-x-x. Declarer must duck the heart switch; then partner will shift back to spades since I returned a high heart.

Steve White: This gives partner [information] to do the right thing (continue the proper major). Trying to knock out the A may lose even when partner has the K; declarer may have three diamonds.

Malcolm Ewashkiw: I’m playing for partner to hold Q-x-x. Leading the 8 (rather than five) puts him in the picture; he’ll know to shift back to spades. … Declarer has a Hobson’s choice: Rise with the A and lose three hearts and two aces; or duck and lose three spades, a heart and the A.

Paul Meerschaert: Hopefully, partner has Q-x-x and goes back to spades after winning the Q. The 8 should steer partner correctly — hopefully. :)

Dale Freeman: Hoping partner has Q-x-x… If declarer ducks the A, partner has to revert to spades; then we have five tricks.

Frances Hinden: If declarer ducks this, I want partner to switch back to spades — hence the 8. The  5 would look like I want a heart continuation.

Bob Boudreau: Looks like declarer will have to duck, and I want partner to return a spade… then we get three spades, one heart and one diamond.

Leonard Helfgott: Partner is highly unlikely to hold the K; but if he has Q-x-x and can be encouraged to shift back to spades, we have it set.

Sim Therrell: I hope partner has Q-x-x and reads my high heart as not desiring a heart return, and goes back to spades.

Norm Gordon: … [As little as] Q-x-x in partner’s hand will do the job… The 8 discourages an immediate heart return, so partner hopefully will pick up on this and continue spades. … If declarer hops with the A, then partner hopefully will return a heart after I win the A and lead a low heart to his queen — else we may be the ones bringing gifts.

Siew Chuan Tan: To discourage partner from continuing hearts if he has Q-x-x; a switch back to spades will defeat the contract.

Richard Morse: Difficult choice between trying to set up a fifth trick (in spades or hearts) or trying to stop dummy’s diamonds by leading a club… I like the 8, hoping partner will take the Q…and switch back to spades. …

Connie Delisle: I need partner to win the Q and return a spade. Declarer should have the K, K and A-J (with A-Q he would bid 3 NT himself). …

Douglas Dunn: If partner wins, he should go back to spades.

Problem 5

Matchpoints	K 9 3		West	North	East	South
Both vul	K 3		Partner	Dummy	You	Declarer
	J 9 3 2					2
	K 9 4 3		Pass	4	Pass	Pass
		A 2	Pass
Lead: K		A 10 6 4
		Q 6 5 4
4 South		J 8 2

Trick	Lead	2nd	3rd	4th
1. W	K	2	6	7
2. W	5	K	A	8

Your Next Lead	Award	Votes	Percent
Q	10	94	11
4	9	350	41
4	6	225	26
A	4	144	17
2	3	13	2
2	2	28	3

Wow. The appearance of dummy almost calls for a sanity check on North. Or is this the return of Fritz? If 4 makes, you might as well place a sign on your forehead: Take me, I’m yours. Alas, even down one might not be a good score, because it appears you can make a heart partial, and many East-Wests will be allowed to play there. You may need to beat this two.

What’s up with the defense? You asked for a diamond continuation, yet partner switched to a heart. South’s 8 suggests partner has five hearts, and the play of the king suggests declarer may have misguessed. No, that doesn’t mesh. Partner would hardly risk a heart lead from the queen after you encouraged diamonds; but it would be safe from the jack. Therefore, it is logical to place South with the Q.

“I have no gift to bring, pa-rum pum pum pum.”

Your lead at this point doesn’t seem crucial, but there are dangers: One possibility, however remote, is that South holds Q-10-8-x-x-x Q-8-2 x-x A-Q, in which case the contract will make if you fail to cash your diamond trick. Ouch. That’s one scenario you couldn’t bear, especially when South chimes in with, “Nice bid, partner.” If you have a club or heart trick coming, it won’t go away; so a diamond return seems in order. Besides icing the setting trick, it also gains in a typical layout like the following:

Matchpoints	K 9 3		Trick	Lead	2nd	3rd	4th
Both vul	K 3		1. W	K	2	6	7
	J 9 3 2		2. W	5	K	A	8
	K 9 4 3		3. E	Q!	8	10	3
6 4		A 2	4. E	4!	8	A	9
J 9 7 5 2		A 10 6 4	5. S	J	4	3	A
A K 10		Q 6 5 4	6. E	5!	10	2	J
Q 7 6		J 8 2		Declarer fails (down 2)
	Q J 10 8 7 5
	Q 8
	8 7
4 South	A 10 5

If you return a heart, declarer will force out the A and eventually establish the fourth diamond* for a club discard, escaping for down one. If you lead and continue diamonds, the established trick in dummy does declarer no good, as you will kill it with another diamond when you win the A. This achieves the desired two-trick set, as well as a lesson for North.

*West has to win the A on the second round, then the J is led through East to smother the 10. This is not double-dummy, as the diamond layout is marked. Declarer knows that East has the Q from the signal at Trick 1; and that West is shorter, else he would duck the second round.

Which diamond should you lead? With proper defense it doesn’t matter, but the queen is surely better.* If you lead a low diamond, you rely on partner to continue diamonds, which is less obvious since he will not expect you to have the A. This reminds me of my Dad (sadly lost in 1979) whose favorite words of advice were, “If you want something done right, do it yourself.” Even so, I feel obliged to award the 4 a close second, as partner should return the suit after your high-low, since you could have a doubleton.

*It might seem that leading the Q could cost if South ruffs, leaving West with the sole diamond protection; but this is superficial. I couldn’t come up with any scenario where declarer could benefit. East can always protect clubs if necessary in the end position.

What about a trump shift? The only case for this would be if South is 6-4 in the majors (e.g., Q-J-10-x-x-x Q-x-x-x 7 A-x) but that doesn’t gel with declarer’s heart play. With Q-9-8-x (or even Q-8-x-x) he could succeed by playing low from dummy to force your 10; then partner’s jack would ruff out. Further, it speaks horrors of partner’s heart shift, which effectively gave away the contract with no redeeming benefit. No, if a trump switch is right, you’re playing in the Little Leagues.

The worst lead must be a club, as breaching the club suit offers several opportunities to lose, and I don’t see any real upside. Even if you’re lucky enough to find partner with Q-10-x, it gains nothing over a diamond return.

Comments for the Q

Leif-Erik Stabell: I have to play a diamond if South is 6=3=2=2 with the Q and A-Q… Since partner might not know to play a third diamond for a second undertrick with x-x J-x-x-x-x A-K-10 Q-10-x, I better play two rounds myself, then another when in with the A. Plus 200 might be important since we are cold for 3 on this layout — although 3 will probably be the popular contract.

Dean Pokorny: The objective is to get 4 two down for a nice plus 200, preventing declarer from establishing a diamond for a potential club discard. Suppose South has something like Q-J-x-x-x-x Q-8 8-7 A-10-x. The safest defense is the return of Q and another diamond, giving partner no chance to err — except a revoke. :) When declarer leads a spade, I win and shoot back the last diamond…

Zahary Zahariev: If we can lose anything, it is a diamond. It looks that South has Q-x-x and A-x-(x), possibly with the Q too. Why the Q? If I find South with J-10-x-x-x-x Q-x-x 10-x A-Q, we must play a third diamond; then a fourth (after the A) for a trump promotion and two down. Maybe partner can’t see this.

John Reardon: It looks as though partner has five hearts. … Almost certainly we can make 3 , so [we need] plus 200 for a good result. Surely the idea is to help partner do the right thing… If South has Q-J-10-x-x-x Q-8 10-7 A-10-x,…our club winner may be lost if I return a low diamond — partner (with x-x J-x-x-x-x A-K-x Q-x-x) [might] switch, expecting me to have the A, not the A. … There seems to be no downside to leading the Q.

Imre Csiszar: Leading trumps wins if South has Q-x-x-x (which must be exactly Q-8-7-2) x A-x; but it loses if he has Q-8 x-x A-Q-x, or Q-8-2 x-x A-Q, which is more likely. The  Q and two more diamond leads ensure down two if South has x-x A-x-x.

Tim DeLaney: If partner has A-K-10, we must play four rounds of that suit to ruff away the potential diamond winner. I am playing declarer for Q-J-10-x-x-x Q-x x-x A-x-x. It is important to beat 4 two tricks, since we can make 3 .

Carsten Kofoed: Then a third and a fourth diamond can give us plus 200.

Charles Blair: I would not have Q-10-8-x-x-x Q-8-2 x-x A-Q, but this South bids like a maniac. If he has Q-J-10-x-x-x Q-8 x-x A-10-x, I know we should continue diamonds, but partner may not.

Rob Stevens: It isn’t clear how many red-suit winners we have, but this subtle play keeps all options open and averts partner from making a mistake in switching to [clubs]. If the Q holds, I can lead another; then a fourth round when in with the A to prevent a discard.

Marcus Chiloarnus: It is possible to fail in many ways; while to succeed is possible only in one way.

Lajos Linczmayer: The play suggests that South has the Q. (If South had Q-J-10-8-7-6 J-x-x 7 A-Q-x, partner’s heart lead would have given him the contract.) If he has Q-J-10-8-7-6 Q-8-2 8-7 A-Q, a diamond return is vital; and if Q-J-10-8-7-6 Q-8 8-7 A-10-x, we must play a third and fourth diamond to score 200.

John Lusky: Declarer must have the Q or J, and I will assume the queen since we are probably getting a great score already if he has the jack. I need to play a diamond now in case declarer has Q-J-10-x-x-x Q-8-2 x-x A-Q. Since partner does not know I have the A rather than the A, he might shift to clubs with disastrous results if I lead a low diamond. If the Q lives, a third round then a fourth round when in with the A will yield plus 200 if declarer has Q-J-10-x-x-x Q-x x-x A-x-x. If South has a stiff diamond, we probably can’t make 3 , and plus 100 will still be good — on that layout my J will protect partner from a possible minor-suit squeeze…

Steve White: Best to take command of the defense, rather than risk partner shifting to clubs.

Chris Willenken: If South is 6=2=2=3 with A-10-x, I need to play four rounds of diamonds before trumps are drawn to kill the discard…

Sim Therrell: Pedestrian to return partner’s suit, I know, but I want to go plus on this hand.

Ed Barnes: It seems declarer might have A-Q doubleton and would like to void dummy in hearts for communication.

Comments for the 4

Manuel Paulo: By instinct and exclusion. … It is wrong to lead a trump if South is similar to J-8-7-6-5-4 Q-9-8-2 7 A-Q; or a club if he has Q-J-10-x-x-x Q-8-2 7 A-10-x.

David Grainger: If declarer has A-Q and the Q, a diamond trick may vanish; while if declarer has a singleton diamond and partner the Q (which I don’t think is all that likely), the heart can’t go anywhere.

N. Scott Cardell: Partner may well have three diamonds (A-K-10 or A-K-8). … If declarer has a singleton diamond and no Q, he has no way to get a discard; but if he has Q-10-8-x-x-x Q-8-2 x-x A-Q, any non-diamond lets declarer unblock the clubs and ruff a heart for a diamond discard. …

Neil Morgenstern: I don’t get partner’s heart switch, except that he doesn’t know I have the Q. Declarer shouldn’t have four hearts, but you can’t be too sure; and he may have started with two diamonds and the stiff A, so let’s get the diamond trick now before it runs.

Rolf Mattsson: Declarer might be able to throw a diamond on the K if he has A-Q doubleton.

Gabriel Ip: … In the face of uncertainty, play passively.

But in the face of passivity, play is uncertain.

David Caprera: This looks like a hand where all we need to do is avoid an accident.

Frances Hinden: I want two undertricks, while not letting the contract through. Declarer may be able to set up a diamond trick eventually, but I can get partner to ruff it out as long as we keep playing diamonds. While a club [might] also set up a second undertrick, it may let the contract through on a very bad day.

Albert Ohana: I am afraid declarer has a second diamond loser and may discard it on the K, entering dummy by ruffing a heart.

Michael Dimich: South is begging for a heart continuation so he can win the Q, A-Q, then ruff a heart and pitch a diamond on the K.

Hans Holme: Partner cannot have Q-J, and I think he holds the jack. A club return is too dangerous, and declarer should handle spades himself; therefore, I return a diamond…

Jing Liu: Declarer must have the Q (from his play of the king) along with Q-J-x-x-x-x and the A. …

Robert Lusis: Declarer has nowhere to discard a heart but [might] discard a diamond…

Problem 6

Matchpoints	Q		West	North	East	South
N-S vul	Q 6		Partner	Dummy	You	Declarer
	Q J 10 8 4 2					2 NT
	Q 5 3 2		Pass	4 1	4	6 NT
		A 10 9 8 7 6 5 4	Pass	Pass	Pass
Lead: J		10 2
		3	1. Gerber
6 NT South		10 9

Trick	Lead	2nd	3rd	4th
1. W	J	Q	?

Your Defense	Award	Votes	Percent
B. Win A, lead 10	10	280	33
C. Win A, lead 2	9	62	7
A. Win A, lead 10	8	197	23
E. Win A, lead 10	5	73	9
D. Win A, lead 3	4	14	2
F. Duck the first trick	3	228	27

Well, here we go again. North’s decision to use Gerber without an ace or king is dubious at best, and South doesn’t even bother to answer but just bids the slam in notrump.* If they make this, you can probably count your matchpoints on one finger or less.

*At matchpoints, South’s 6 NT bid is a reasonable stab since partner could not know about the K. Further, many partnerships lack a clear understanding of coping with interference over Gerber, so South may have just taken the safety play of bidding what looked right.

“A new born King to see, pa-rum pum pum pum.”

Counting the missing points shows partner must have at least a king (South would be too strong for 2 NT with K A-K A-K and A-K). If it’s the guarded K, declarer is always going down — unless you duck the first trick, only to find partner having no more spades. Ouch! While ducking could produce a mammoth set (down seven), it is hardly worth the risk since few will bid this slam.

Some respondents felt that ducking the first trick might be necessary to avoid rectifying the count for a squeeze. While certainly true, this does not take into account declarer’s other resources. Consider this deal:

Matchpoints	Q		Trick	Lead	2nd	3rd	4th
N-S vul	Q 6		1. W	J	Q	9?	3
	Q J 10 8 4 2		2. N	2	3	A	7
	Q 5 3 2		3. S	5	9	Q	4
J 2		A 10 9 8 7 6 5 4	4. N	4	5	K	4
K J 8 7 4		10 2	5. S	6	7	J	6
9 7		3	6. N	10	7	3	8
J 8 7 4		10 9	7. N	8	8	5	2
	K 3		8. N	2	9	A	4
	A 9 5 3		9. S	K	7	3	10
	A K 6 5		10. S	6	8	Q	10
6 NT South	A K 6		11. N	5!	2	K	J

If you win the A and return a heart, West is eventually squeezed in hearts and clubs, so suppose you duck. Declarer will run diamonds (pitching two hearts) forcing West to discard his remaining spade* to keep clubs and hearts guarded. Then three rounds of clubs ending in dummy reveal West has a stopper, and declarer will exit with a club for the heart endplay.

*West might make it more difficult by blanking his K, but declarer should still get it right. East would hardly duck with nine spades, nor with the K; so the indicated play is to drop the king.

On this layout the killing defense is to win the A and return a spade, which breaks up the positional squeeze against West by squeezing dummy. Note that if a heart is pitched from dummy, East can guard hearts with 10-2, so West is relieved.

The spade return was my intended solution when I created this problem, but it’s not a cure-all. The deal might instead be:

Matchpoints	Q		Trick	Lead	2nd	3rd	4th
N-S vul	Q 6		1. W	J	Q	A	3
	Q J 10 8 4 2		2. E	10?	K	3	2
	Q 5 3 2		3. S	A	5	2	3
J		A 10 9 8 7 6 5 4	4. S	K	6	4	4
J 9 7 4 3		10 2	5. S	A!	4	3	9
9 7 6 5		3	6. S	5	4	Q	2
K J 4		10 9	7. N	Q	5	6	7
	K 3 2		8. N	J	6	7	9
	A K 8 5		9. N	10	7	8	J
	A K		10. N	8	8	2	?
6 NT South	A 8 7 6			West is squeezed

Declarer will win the K (pitching a club); unblock the A-K; cash the A (Vienna coup); cross to the Q and run diamonds to squeeze West in hearts and clubs. Only a heart return will defeat the slam.

A heart return is also necessary when South has K-3-2 A-x-x-x A-K-x-x A-K, as failure to do so gives declarer a double squeeze with hearts as the common suit.

So which return (spade or heart) is better? I didn’t know, so I ran a 1000-deal simulation. Results were extremely close; only two deals separated the options, which was hardly conclusive for the sample size.

Then I realized that my conditions for my simulation were unfair. I had bequeathed South the three missing aces, but this is hardly cast in stone. South might bid the same way with K-x K-J-x A-K-x A-K-x-x-x, in which case partner’s A goes to sleep if you don’t return a heart. Therefore, I ran another simulation giving South either a maximum 2 NT bid (21-22 HCP) or a five-card suit; i.e., something extra to justify the 6 NT bid but without regard to aces. This showed a definite edge for the heart return, so it gets the top spot.

Which heart? It makes no difference if South has the three missing aces; but the 10 is necessary if South has K-3 A-K-9-8-x A-K-x K-J-x. I would like to award second place to the spade return, but the simulation doesn’t support it; the 2 fared better. Oh well; so my original answer is demoted to third place. C’est la vie.

Other choices are much inferior. A club return does nothing in regard to squeeze defense; its only real benefit is to find partner with the A when declarer has five running hearts. A diamond return lacks any benefit besides the fact you won your A. Worst of all is to duck the first trick. Imagine your anxiety when partner wins the next trick with the A — either down seven or making, depending on whether partner has another spade; or even worse, partner starts thinking about your high spade being suit preference for hearts. Talk about pressure! Hopefully you won’t have a coronary in the meantime.

Comments for B. Win A, lead 10

Leif-Erik Stabell: This will prevent partner from being squeezed on many layouts, particularly if South has A-K bare in one of the minors. It’s hard to see that the 2 can be any worse, but perhaps K-3 A-K-9-8-x A-K-x K-J-x is possible.

Dean Pokorny: We can beat 6 NT…if declarer holds A-K doubleton in one of the minor suits, say, K-x-x A-x-x-x-x A-K-x A-K. I must immediately return a heart to break declarer’s entry for a squeeze; and it is better to return the true card because I don’t need the 10, and partner can easily read it as a doubleton and visualize better the whole layout.

Zahary Zahariev: No way to gain anything by ducking — partner will be endplayed. To have chances, declarer must have the K, A, A-K, A and one more king. There are three hands where I can do something: (1) K-x A-x-x-x A-K-x-x A-K-x (without jacks), (2) K-x-x A-J-x-x A-K-x-x A-K, and (3) K-x-x A-K-x-x A-K A-J-x-x. Against Hand 1, I must return a spade to squeeze dummy; but against both 2 and 3, only a heart kills the squeeze. … Which heart? There is no matter, but why help declarer if he has K-x-x A-K-9-8 A-K-x A-J-x — he must decide who has the K (squeeze or finesse).

Manuel Paulo: I win the A because the jack may be a singleton. …Partner must hold [at least] a king. … If partner’s hand is similar to J-x J-x-x-x-(x) 9-7-6-5 K-x-(x), declarer wins 12 tricks on a heart-club squeeze unless I lead a heart to destroy it. To avoid any error by partner, I lead the 10.

Bruce Neill: Declarer should have three aces to jump to slam, and partner has a king… The danger is that partner has the K and will get squeezed between that and his long hearts. If diamonds are blocked (say South has K-3-2 A-K-9-8 A-K A-J-8-7), I can break up the squeeze by switching to a heart…

Carsten Kofoed: This can seriously disturb their communication lines; South could have K-3-2 A-K-9-8 A-K A-J-8-x.

Charles Blair: I keep worrying that South has five hearts and no A. A slight advantage for the 10 over the two is giving declarer more losing choices with K-x A-K-9-8 A-K-x A-J-x-x.

N. Scott Cardell: Declarer must have three aces and three kings, and possibly one of the missing jacks as well. … If partner has the K, I must lead a heart to break up the squeeze should diamonds be blocked. If declarer has something like K-x-x A-K-9-8 A-K A-J-x-x, only the 10 will do. Ducking the first trick will not work against a rounded-suit squeeze; the queens in dummy guarantee a strip squeeze any time a simple squeeze would exist with the count rectified. …

John Lusky: If declarer has K-x A-x-x-x-x A-K-x A-K-x, it is right to continue spades to force a premature discard from dummy. However, there are…more hands where a heart switch is needed. If declarer has K-x-x A-9-x-x-x A-K A-K-x (or A-K-x A-K), a heart breaks up a double squeeze; or against K-x-x A-K-x-x-(x) A-K A-x-x-(x), it breaks up a heart-club squeeze. I lead the 10 in case declarer has K-x A-K-9-8-x A-K-x K-J-x.

Julian Wightwick: I guess that declarer has three aces and three kings to justify his jump. … One chance I can see where my play makes a difference is if declarer has something like K-x-x A-J-x-x A-K-x-x A-K, in which case a heart switch scrambles his communication. I’ll lead the 10 to protect partner’s possible J-x-x-x…

Weidong Yang: Ducking the first spade is out of the question. South should have K, A, A, A and two other kings for his bid. I don’t worry if partner has the K. If partner has the K or K, he will be squeezed in most situations — except if declarer has A-K doubleton [in a minor]. The  10 is the boat to help partner escape the torrent of a squeeze.

Barry Rigal: The duck looks attractive if declarer has K-x A-K-x-x A-K-x A-x-x-x, as it [offers a losing option to endplay me instead of partner]; if I win…partner will always be squeezed. I’ll play declarer for K-x-x A-K-x-x A-K A-x-x-x, where the heart play breaks up the squeeze. I hope it is not K-x A-K-J-x-x A-K-x K-x-x!

Ken Brantferger: It looks like the [best] hope is for declarer to hold A-K tight, in which case this may prevent him from [executing] a heart-club squeeze.

Toby Kenney: Saves partner from the squeeze if…either minor suit is blocked.

Julian Pottage: I must win in case the lead is a singleton, and I switch to hearts in an attempt to break up a heart-club squeeze if South has A-K bare in one of the minors. The  10 is better if South has A-K-9-8-(x).

Frances Hinden: I’ll chew up declarer’s entries [hoping] to prevent a coming squeeze; the 10 in case he has A-K-9-8.

Albert Ohana: If declarer is missing a rounded king, I try to disturb his communication for the heart-club squeeze he may construct against partner.

David Stern: It is just possible declarer is off two aces and can make six diamonds, five clubs (equally five hearts) and a spade. If so, they are more likely to be off the A [than the A].

Dirk Enthoven: Ducking the spade is nonproductive, as the only impression it might create is that I have no entries. … A heart or a club lead might help us, and a heart seems more rewarding.

Bogdan Mitran: It is possible to break a squeeze in hearts and clubs if South has something like K-x-x A-K-x-x A-K A-J-x-x — or maybe we have to take the A before South cashes six diamonds, five clubs and a spade. :)

Alon Amsel: If declarer holds something like K-x-x A-K-x-x A-K A-x-x-x, I have to break communication so partner cannot be squeezed in clubs and hearts.

Connie Delisle: It feels right not to let declarer rectify the count; but partner (with long hearts and the K) will feel the pressure either way. …

Junaid Said: This beats it when declarer has something like K-x A-K-9-8-x A-K A-x-x-x…

Comments for C. Win A, lead 2

Kevin Lewis: I don’t duck the first trick — even if it is Christmas. :)

Richard Morse: … Ducking seems out; this does not feel the right time to gamble on partner having another spade. There can be no hurry for a diamond lead; but any of the others might be right. Assuming declarer has a spade and six diamonds in the bank, five running clubs seems likelier than hearts.

Comments for A. Win A, lead 10

John Reardon: South may have something like K-x A-9-x-x A-K-x-x A-K-x, in which case the only defense is to lead another spade now to squeeze dummy…

Tim DeLaney: This squeezes dummy out of a heart and beats the contract when declarer has K-x A-x-x-x A-K-x-x A-K-x (my 10 comes into play). … Choice F is calamitous if South had K-x-x A-K-x-x A-x-x A-K-x.

Sylvain Brethes: I’ll try to squeeze dummy at trick two.

Marcus Chiloarnus: Last Monday I played for a complete top by ducking. Unfortunately, we came last.

Lajos Linczmayer: In the critical case South has K-x A-9-x-x A-K-x-x A-K-x, and West will be squeezed in clubs and hearts. The holdup play doesn’t help (a throw in comes); but a spade return squeezes dummy.

Sid Ismail: This kills it if South has K-3 A-x-x-x A-K-x-x A-K-x — [squeezing dummy] so declarer will play for 3-3 clubs now (a stiff K is unthinkable). …

Herbert Bruch: Squeeze the dummy (declarer must pitch a heart or club). Partner can infer you have at least 10-x and blank his K if he holds K-J-x-x-(x) J-x-x-x. …

Sneha Sridhar: Break the positional squeeze against partner in hearts and clubs by forcing declarer to discard from dummy [prematurely].

Nick Krnjevic: Partner not only has a king somewhere but must also guard both hearts and clubs. … If declarer has something like K-x A-x-x-x-x A-K-x A-K-x, I must return a spade to squeeze dummy…

Neil Morgenstern: Ducking the first trick could lead to a spectacular set if partner started with J-x and the K, but I need to be a bit more sensible. Winning the ace and leading another spade knocks out what could well be a squeeze [threat] against partner, who has the K and J-x-x-x. If this is the situation and I duck the first trick, partner will be [squeezed and endplayed].

Gabriel Nita-Saguna: Partner is marked with a king… If he has K-J-x-x-(x) and J-x-x-x, I must hope declarer started with only two spades (otherwise he could develop a double squeeze). Returning the 10 squeezes dummy irremediably. Assuming declarer discards a heart, I will hang on to my 10-x to allow partner to guard clubs.

Malcolm Ewashkiw: Hoping to squeeze dummy at trick two, playing partner for K-J and J-x-x-x. Note that if declarer holds K-x A-K-x-x A-K-x-x A-x-x, partner had to lead a heart to defeat the slam.

David Caprera: Force declarer to make his pitch [from dummy]. Leading a round suit may tell declarer how to play the hand.

Tim McKay: If this really is a gift horse, then I won’t look it in the mouth.

Sven Pride: Force an early discard from dummy [hoping to prevent] partner from getting squeezed with the K and J-x-x-x. Ducking the first spade doesn’t help because six diamonds followed by four clubs will endplay partner.

Dale Freeman: The 10 could be correct if declarer has blockage in diamonds [or clubs]. However, I think declarer is more likely to have K-x A-x-x-x A-K-x-x A-K-x; then a spade back forces a heart discard, and my 10-x will be golden.

Chris Willenken: Force declarer to discard from dummy before he can squeeze partner in the rounded suits.

Michael Dimich: The 10 forces a heart discard; now declarer’s only hope [with A-9-x-x A-K-x] is that West started with K-J-10-x-x. Unlucky for South, my 10 wins the last trick.

Hans Holme: Squeeze dummy before partner, in case partner holds K-J and J-x-x-x. …

Ed Barnes: Declarer must throw a card from dummy, which may save me from feeling sorry for partner later in the hand.

Gerald Cohen: Trying to squeeze dummy. If partner has K-J and J-x-x-x, this is the only defense that works — though I had better not throw a heart. :)

Douglas Dunn: …This may squeeze dummy at trick two, forcing a heart discard. Hang onto that 10!

Final Notes

I hope you enjoyed my Christmas contest — or for those of other faiths, at least put up with it and not feed us to the lions. Thanks to all who entered, and especially those who offered holiday greetings and/or kind remarks about my web site.

Comments are selected from those above average (top 427 in this edition) and on each problem only those supporting the correct solution or close seconds. While this might be considered biased, I feel it’s the best way to ensure solid content and avoid potential embarrassment by publishing comments that are flawed. On this basis, I included over 70 percent of the eligible comments. If you supplied comments that were not used, I thank you for the input.

Use of a comment does not necessarily mean I agree with it, but generally they are all worthy. Comments are quoted exactly except for corrections in spelling and grammar. Where I have included only part of a comment, an ellipsis (…) indicates where text was cut. Text in [brackets] was supplied by me to summarize a cut portion or fix an omission. Comments are listed in order of respondents’ rank, which is my only basis for sequencing. I am confident that my lengthy study of these problems, assisted by comments received, has determined the best solutions in theory, but oversights are possible. Feedback is always welcome.

“Then He smiled at me, pa-rum pum pum pum.”

Well, it’s about time for the drum rehearsal,
so our little drummer boys will finish it up:

Dale Freeman: I am sure I was generous with gifts! Ho Ho Ho!

Marcus Chiloarnus: Some of my comments are wise, and some are otherwise.

Bill Cubley: Winning this would be better than getting a pony for Christmas. Can I bribe Richard with some cookies? It always worked with Santa Claus when I was young.

Howard Dean: Am I weak on defense?

Does a reindeer have hooves? [Checks the scores] Oops… 52 ain’t shabby!

Analyses 7X64 Main Challenge

Scores Top Our Finest Gifts We Bring

Credits to K. Davis, H. Onorati and H. Simeone, lyricists of “The Little Drummer Boy”
© 2003 Richard Pavlicek