Puzzle #18

Inferential Problem

by Kit Woolsey

 NORTH ♠ A 7 5 ♥ A Q 10 ♦ A J 3 ♣ 8 6 4 2 SOUTH ♠ Q J 8 6 ♥ 9 7 2 ♦ K 6 5 ♣ A K 9

South, who has the best poker hand, can make six spades against any defense.

What are the exact East-West hands?

Solution

 NORTH ♠ A 7 5 ♥ A Q 10 ♦ A J 3 ♣ 8 6 4 2 WEST ♠ K 4 3 2 ♥ K J 8 ♦ Q 10 8 ♣ 7 5 3 EAST ♠ 10 9 ♥ 6 5 4 3 ♦ 9 7 4 2 ♣ Q J 10 SOUTH ♠ Q J 8 6 ♥ 9 7 2 ♦ K 6 5 ♣ A K 9

Neither defender can have five spades (else South's straight would not be the highest-ranking poker hand). East must hold ten-nine doubleton of spades, and the contract is made on a smother play. South wins the opening club lead (best), takes the queen and jack of trumps, wins a heart finesse, leads a club to the closed hand, wins another heart finesse, cashes the ace of hearts and three diamonds, then leads a club to force East on lead to play a red card, smothering West's king of spades.

East's clubs must be queen-jack-ten, else he can unblock; the rest of the red-suit cards can be deduced from the condition that South holds the best poker hand.