Puzzle #7

Big Cassino and Little Cassino

by Jeff Rubens

In an inferential problem (a form introduced in Puzzle # 3), deductions about unseen hands (in some cases, the exact cards) can be drawn from nonstandard clues. The conditions are often weird, but when untangled they generally lead to an interesting point of card play.

 NORTH ♠ 3 ♥ 9 6 4 ♦ A 7 6 ♣ K Q 9 5 4 2 SOUTH ♠ A Q 9 5 4 ♥ 3 2 ♦ K 9 5 3 ♣ A 10

South is declarer at a contract of six diamonds. After the lead of any black card, South can make his contract; after the lead of any red card, perfect defense can defeat the contract. With spot cards defined as cards from deuce through ten, the sum of East's spot cards in hearts subtracted from the sum of East's spot cards in diamonds is exactly one-third of the sum of East's black spot cards. Neither defender is void of hearts, and neither holds both big cassino (diamond ten) and little cassino (spade deuce).

What are the exact East-West hands, and how does South fulfill the contract after a favorable lead?

#### Solutions

This is a summary of a chain of deductions that could be made to determine the defenders' hands.
As neither defender is void of hearts, South must discard all his hearts before losing the lead. Further, declarer cannot lose a trick to one of the three missing low trumps. If diamonds are 3-3, no discards can be taken. Therefore, diamonds must be 4-2, with West holding two honors. Then, declarer can obtain two discards on the clubs in dummy. These discards must be taken after two trumps are drawn; therefore the spades must be establishable with one ruff in dummy. East must hold K-J-10 blank in spades. Also, his four clubs must include the jack, as the black-suit lead can help declarer only by providing an entry for a black-suit finesse (by actually taking a finesse). Since the sum of East's black-suit spots is divisible by three, East holds J-8-6-3 in clubs. Since West holds the spade deuce, East's diamond honor is the ten. Therefore, East holds two hearts with a spot total of 15, and the East-West hands are:

 WEST ♠ 8 7 6 2 ♥ A K Q J ? ? ♦ Q J ♣ 7 EAST ♠ K J 10 ♥ ? ? ♦ 10 8 4 2 ♣ J 8 6 3

After a black-suit lead, declarer wins cheaply, cashes the diamond king-ace, takes the remaining black-suit finesse, clears the remaining black winners, ruffs a spade in dummy and discards two hearts on two winning clubs. Clubs are continued. If East ruffs low, declarer overruffs and plays high spades. If East never ruffs, a trump coup position is reached at trick 12. East's two hearts must be 10-5, not 8-7, because in the latter case an opening lead of the heart five would not defeat the contract.