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Lilliputian Squeezes

Over the holidays I took a Caribbean cruise with my wife, including a stopover at Lilliput for a bridge seminar. Upon docking at the island, Mabel and I were transported by handheld carriage to the bridge studio, where over 1000 students were seated and waiting. My lecture topic on squeeze plays seemed especially appropriate, as I marveled over the tight arrangement of 256 mini tables on 18-inch centers, each with a tiny watering can of flowers, and playing cards the size of confetti. Everything was cozy. I didn’t even need a microphone.

After the lecture we agreed to play a round of Lillago (miniature four-deal bridge) against Tim and Lilly, their best pair. The setup was a bit awkward, as I accidentally crushed a table, and Mabel trampled a kibitzer, but we were soon under way with nary a fatality. On the first deal Lilly (North) opened 1 C, Mabel overcalled 1 H, and Tim bid 1 NT which Lilly raised to game. Rather than lead my love’s suit with a singleton, I decided to attack with my own. The appearance of dummy was quite a shock; if this is their “best pair,” Tim must be a genius.

3 NT S A K 6 2
H 10 9 6
D K 10 4
C K J 2
Leader
1. W
2. E
3. N
4. S
5. E
6. N
7. E
8. N
9. S
10. E
Lead
C 10
C 8
H 10
D 7
S 8
D K
S 7
H 6
D 5
H K
2nd
J
6
J
9
10
A
9
7
C 7
A
3rd
A
9
Q
10
J
6
Q
8
4
C 4
4th
5
K
5
Q
K
J
A
C Q
8
9
S Q J 5 4
H 5
D J 9
C Q 10 9 7 4 3
Table S 8 7
H K J 7 4 3
D A Q 8 2
C A 8
Lead: C 10 S 10 9 3
H A Q 8 2
D 7 6 5 3
C 6 5

Mabel captured the C J with her ace and returned the suit, overtaken by me and won in dummy. Declarer took a heart finesse (Mabel wisely covered) and led a diamond to the nine, 10 and queen. Mabel exited safely with a spade, covered around, then Tim smartly led the D K to Mabel’s ace smothering my jack. Another spade was covered by all. Tim now tried a sneaky H 6, but Mabel was right there with the seven to force the eight. Next came the D 5 to drive out the eight, and Mabel returned the H K smothering dummy’s nine. Meanwhile, I discarded my club equals from the top, if only to add flair for the 10 kibitzers perched on my shoulders.

This left the ending shown at the right. Tim next led the D 3, and I was lilli-squeezed — holding only a three, four and five! In fact the whole ending fit the location to a tee, so I jotted down the cards for this article.

Evidently the combined spot-card total of 39 can be equaled in various ways, but it cannot be reduced. I had just witnessed the world’s smallest simple squeeze!
South
leads
S 6 2
H
D
C 2
S 5 4
H
D
C 3
Table S
H 4 3
D 2
C
S 3
H 2
D 3
C

On the next deal Tim and Lilly reached a small slam (is there any other kind here?) in clubs. I don’t remember the exact hands, but Tim was declarer and booked early when we won our ace. After that, he could have claimed several times, but he wasted some high cards, as if on a mission to reach the following ending with South on lead.

Clubs
win 3
S 8 3
H
D 2
C
Leader
1. S
Lead
C 2!
2nd
S 4
3rd
D 2
4th
?
S 5 4
H
D 3
C
Table S 7 6
H 3
D
C
South
leads
S 2
H 2
D
C 2

“Deuces never loses,” Tim asserted as he put his last trump on the table. There I was with another three, four and five, but this time I had help from my girl in spades; or so I hoped as I let one go. The diamond was discarded from dummy, and now Mabel was squeezed as well. Rather than prolong it, she also threw a spade, and dummy’s S 3 won the last trick.

What’s this? Another minuscule end position, and this time we were double lilli-squeezed. Sure enough, checking the spot-card total of 47 showed this to be the minimum possible. We had just experienced the world’s smallest double squeeze.

By this time I was tired from a long day’s travel, and the third and fourth deals are fogged in my memory — even Mabel couldn’t remember the hands (go figure). After the round Lilly offered me a drink from the watering can, and I dozed off to dreams of Tiny Tim trilling “Tiptoe Through the Tulips.” All I remember for sure was witnessing the world’s smallest triple squeeze, first in notrump and then in clubs. Perhaps you can restore my memory by constructing the endings.

Construct the smallest triple squeeze (1) in notrump, and (2) with clubs trump.

For a valid triple squeeze, one defender must be squeezed in three suits, allowing declarer to win all the tricks. The ending may be any number of tricks but obviously fewer is better. Smallness is judged by the rank (ace = 14) sum of all cards used. Try it yourself before reading the winning solutions below.

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Tom Slater Wins!

In January 2015 this puzzle was presented as a challenge, inviting anyone who wished to submit a solution. Wishes weren’t exactly horses, or Lilliputian ponies for that matter, but 24 brave souls entered the fray. Not many, but it sextupled my previous participation. Let me see… [grabs calculator] At this rate I can exceed the world population by December — 8,707,129,344 to be exact.

Congratulations to Tom Slater of Manchester, England, who was the first of only three solvers to produce the minimal spot count for both notrump and clubs. (The fact that his name anagrams to “most alert” may account for this.) Four others came close, missing by a single pip, for places 4-7. Thanks to all who participated!

RankNameLocationNotrumpClubs
1Tom SlaterEngland3736
2Grant PeacockMaryland3736
3Tim BroekenNetherlands3736
4Dan BakerTexas3737
5Leigh MathesonAustralia3737
6Gareth BirdsallEngland3737
7Audrey KuehEngland3737

Solution

As my introduction showed, the spot total of the smallest simple squeeze is 39, and the smallest double squeeze is 47. Therefore, one might expect a triple squeeze to require more. Not so. In fact it even drops below the simple squeeze, as the successful solvers showed.

The key to the smallest solution in notrump is a jettison triple squeeze, which can reduce the sum to 37. Our winner produced the following ending, neatly subjecting West to a four-gone conclusion.

Notrump
win 3
S 5
H 3
D 3
C
Leader
1. S
Lead
C 3
2nd
?
3rd 4th
S 4
H 4
D 4
C
Table S
H 2
D 2
C 2
South
leads
S 3 2
H
D
C 3

Tom Slater: South leads the C 3 to triple-squeeze West. [If he pitches the S 4, North jettisons the five to leave the South hand high]. I couldn’t see a way to reduce it to 36, as anything that I tried had entry problems.

Yes, you can’t squeeze blood out of a rock; 37 it must be. Another respondent offered these sage words:

Dan Baker: I think the jettison squeeze is the only three-trick triple squeeze that can be achieved in notrump due to transportation issues.

Trumps make a difference

The previous ending works just as well with clubs trump, so one might conclude that no improvement is possible in a suit contract either. Curious game, this bridge. The presence of a trump suit allows the ultimate solution, a scant 36. This has to be the smallest possible, since a triple squeeze requires at least three tricks, and the 12 lowest spot cards (4-3-2 in each suit) demand 9 × 4 = 36.

The key to the solution in clubs (or any trump suit) is a backwash squeeze of the barest kind. Here is the ending from second-place finisher Grant Peacock, who also earns style points for ruffing a winner to inflict the squeeze. Forgive me, but it does him proud.

Clubs
win 3
S
H 3
D 3
C 4
Leader
1. S
Lead
S 4
2nd
2
3rd
C 4
4th
?
S 2
H 2
D 2
C
Table S
H 4
D 4
C 2
South
leads
S 4 3
H
D
C 3

When declarer ruffs a spade in dummy, East is triple-squeezed. If he discards a trump (underruffs), the South hand is high; and whichever four he discards establishes dummy’s three, which is led next to force his trump.

Pushing the conditions

Lastly is the following entry from Tim Broeken. Besides being my all-time leading puzzle solver, he has the Hitchcockian knack of delivering the unexpected. True to colors:

Clubs
win 3
S 3
H 3
D
C 4
Leader
1. S
Lead
D 4
2nd
?
3rd 4th
S 4
H 4
D
C 3
Table S 2
H 2
D 3
C
South
leads
S
H
D 4 2
C 2

When South leads the good diamond, West is triple-squeezed. Or is he? While it’s true that any discard (including a trump) allows South to win the rest, West’s fours are irrelevant. If East had both fours and West both twos, declarer still wins three tricks by leading good diamonds until West ruffs. Whether this qualifies as a “triple squeeze” by my stated conditions is arguable, but since it didn’t decide the winner, I’ll let it slide for third place.

Time to come home

Mabel: Hurry, dear, or we’ll miss the boat. And watch your step! There’s four little guys playing bridge by your left foot…

Oops. [squash] Help!

Mabel: Shall I call 911?

No, just add up the pieces. This might be the smallest quadruple squeeze.

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© 2015 Richard Pavlicek