Puzzle 8K10   Main


One Foggy Christmas Eve


  by Richard Pavlicek

Santa came to say…

“Rudolph with your nose so bright, did you set this slam tonight?”

“Six spades they tried,” the reindeer replied, “I led a heart and declarer was fried.”


“I see,” said the master of Yuletide arts, “But what if the slam is played in hearts?”

“No!” cried Rudolph, about to stampede, “That’s even set if a trump is the lead.”

On Christmas morning the fog lifted, but only the North-South cards remained:

6 S South
Both Vul
S Q 9 8 7 6 5
H K 10 9 8 7
D
C 9 2
Rudolph
West

Pass
Pass
Pass
Pass
Donner
North

2 D
3 H
6 S
Ronald
East

Pass
Pass
Pass
Blitzen
SOUTH
2 C
2 NT
4 S
Pass
S  ?
H  ?
D  ?
C  ?
TableS  ?
H  ?
D  ?
C  ?
Lead: H S A K J
H Q J 6 5
D A K J 10 5
C A

Help! Nobody can remember the other hands, so it’s up to you:

Construct a West hand for Rudolph that fits the dialogue.

Multiple solutions exist. Further goals (tiebreakers for the December contest) are for the HCP total and spot-card sum (in that order of priority) for West and East to be as near to equal as possible.

Eddy Choi Wins

In December 2010 this puzzle was presented as a contest, with 76 participants from 42 locations. Thanks to everyone who entered, and congratulations to the 25 successful solvers. Ranking is by the most even division of the E-W HCP, secondarily by the most even spot-card sums, and lastly by date-time of entry.

Kudos to Eddy Choi, Hong Kong, who was the first of 11 solvers to give East-West identical HCP totals and spot card sums.

Winner List
RankNameLocationHCPSpots
1Eddy ChoiHong Kong6-655-55
2Charles BlairIllinois6-655-55
3Jonathan MestelEngland6-655-55
4Gareth BirdsallEngland6-655-55
5Manuel PauloPortugal6-655-55
6John AuldEngland6-655-55
7Jim MundayCalifornia6-655-55
8Pavel StrizCzech Republic6-655-55
9Leif-Erik StabellZimbabwe6-655-55
10Julian WightwickEngland6-655-55
11Howard LiuIllinois6-655-55
12Mike ChanterEngland6-653-57
13James LawrenceEngland6-648-62
14Ufuk CotukEngland5-758-52
15Sid IsmailSouth Africa2-1055-55
16Barry RigalNew York2-1055-55
17Paul GilbertEngland10-259-51
18Jan KuipersNetherlands10-251-59
19Richard SteinCalifornia2-1062-48
20Barry GoodmanEngland2-1062-48
21Wayne SomervilleNorthern Ireland2-1063-47
22Ryan LeungSingapore10-247-63
23Sebastien LouveauxBelgium2-1063-47
24Harold GoodmanGeorgia (US)2-1063-47
25Rik ter VeenNetherlands2-1063-47

Puzzle 8K10   MainTop   One Foggy Christmas Eve

Solution

Per the dialogue, the object is to construct a West hand, and thereby a complete deal, in which a heart lead will defeat bothS and 6 H. It is easy to see how 6 S can be defeated by a heart ruff; but if such a layout exists, how could a heart lead defeat 6 H? Indeed, it could not, so a more devious approach is needed.

Ten solvers (places 16-25) went for the brazen solution of a 10-0 club division, allowing the defense to get a club ruff against either 6 H or 6 S. While undeniably valid, this construction requires the H A to be in the same hand as the long clubs for a heart lead to beat both slams, which means a lopsided HCP division and therefore no contention for the top spot. (A 10-card club suit also makes the auction implausible, but this has no bearing on the puzzle solution.)

A more subtle construction allows an equal arrangement of 6 HCP for West and East, as well as an equal spot-card sum of 55. The first solver to submit an optimal solution was Eddy Choi (Hong Kong):

6 S South S Q 9 8 7 6 5
H K 10 9 8 7
D
C 9 2
Trick
1 W
2 E
Lead
H 4
H 3
2nd
7
3rd
A
4th
5
W-L
L1
S
H 4 2
D Q 9 8 7 6 4 3 2
C K J 10
Table S 10 4 3 2
H A 3
D
C Q 8 7 6 5 4 3



Lead: H 4
S A K J
H Q J 6 5
D A K J 10 5
C A
Lose 1 trump trick

Six spades is defeated by the defense shown, since declarer cannot reach dummy to draw the last trump; East must score the S 10. Six hearts is defeated in more straightforward fashion by the imminent spade ruff after any lead (including a trump).

Eddy’s solution was duplicated by Jonathan Mestel, John Auld (can I add Lang Syne? as I write this just an hour into 2011), Julian Wightwick and Howard Liu. Alas, this was not my intended solution — translation: I overlooked it — but of course equally correct.

Howard Liu: Neat puzzle! Nice usage of the C 9 to enforce the tiebreaker, in the spirit of dividing the twelve points of Christmas.

Not sure how to interpret this, but next time I’m makin’ a list and checkin’ it twice!

Intended solution

The solution I intended was submitted by the six of the top 11, including the winner of my last contest, Charles Blair (Illinois):

6 S South S Q 9 8 7 6 5
H K 10 9 8 7
D
C 9 2
Trick
1 W
2 E
Lead
H 2
D 3
2nd
7
3rd
A
4th
5
W-L
L1
S
H 4 3 2
D Q 9 8 7 6 4 2
C K J 10
Table S 10 4 3 2
H A
D 3
C Q 8 7 6 5 4 3



Lead: H 2
S A K J
H Q J 6 5
D A K J 10 5
C A
Lose 1 trump trick

Six spades is defeated by the defense shown, similarly garnering a trump trick for East. It is also curious, though irrelevant to the puzzle, that a heart lead is required to beat 6 S, whereas any lead suffices on the previous deal. Six hearts is defeated with any lead.

African safari

And finally, to avoid possible ambiguity in the instructions, Leif-Erik Stabell (Zimbabwe) left no antlers unturned as he rafted the mighty Zambezi River, producing this layout:

6 S South S Q 9 8 7 6 5
H K 10 9 8 7
D
C 9 2
Trick
1 W
2 E
Lead
H 2
D 9
2nd
7
3rd
A
4th
5
W-L
L1
S
H 4 3 2
D Q 8 7 6 4 3 2
C K J 5
Table S 10 4 3 2
H A
D 9
C Q 10 8 7 6 4 3



Lead: H 2
S A K J
H Q J 6 5
D A K J 10 5
C A
Lose 1 trump trick

Leif-Erik Stabell: This assumes high cards are included in counting spots as ace = 1, king = 13, queen = 12, jack = 11, etc. If high cards are included but ace = 14, swap the D 9 and D 3, in which case East-West cannot have the same spot count. If high cards are not included in the spot count, swap the C 10 and C 5 in addition.

I think I see it now: Three cases covered, two subtle swaps… and a partridge in a pear tree.

Gleefully Yours

Charles Blair: Using the Four Aces Point Count (ace = 3, king = 2, queen = 1, jack = 0.5) your solution fails the “equal HCP” goal.

Wonderful. Instead of a Yuletide with three wise men, I get one wise guy.

Pavel Striz: Merry Christmas, reindeer!

Then all the reindeer loved him, as they shouted out with glee,

“Rudolph the red-nosed reindeer, you’ll go down in his-tor-y!”

Puzzle 8K10   MainTop   One Foggy Christmas Eve

Acknowledgments to song lyricist, Johnny Marks
© 2010 Richard Pavlicek