One bird to a cage by
Long, long ago famous pigeon fancier Dirichlet, a 19th-century German mathematician, was passionately fond of mathematics. He combines his love for mathematics and pigeons into the Dirichlet Theory of Cages. He had observed over many years that you can't place six pigeons in five cages -- no way. Many years later Krzysztof Jassem used the Theory of Cages to help him as declarer when playing bridge. The idea is that if you have determined certain cards are in one defender's hand, and the number of known cards is equal to the number of cards still held, then all other cards must be with the other defender.
Jassem used this theory on this deal that came up during the Polish battles to determine who was going to represent our country in the World Championships in Albuquerque. East-West were vulnerable and South was the dealer.
E/W Vul. Dealer South.
S A 5 4 S K 9 6
H K T 3 H A J 8
D -- D K J 9 8 5 2
C A K J T 9 6 5 C Q
WEST NORTH EAST SOUTH
Jassem Jezioro Oppenheim Russyan
1C 1S 3D Pass
4C Pass 5C Pass
6C All Pass
The opening lead was the queen of spades, taken by the king, and Jessem played a small diamond! Russyan played small and Jassem discarded a small spade from his hand. Jezioro won and continued with the jack of spades to Jessem's ace (I was happy to see that South had a second spade!)
Now Jessem ran clubs, throwing diamonds and the jack of hearts from dummy. Before cashing the last trump the position was:
S -- S 9
H K T 3 H A 8
D -- D K
C 5 C --
Jezioro, South, threw a small heart on the last club and Jassem tossed the spade from dummy. Everyone had three cards left, and Jassem worked out what was in the three cages held by Jezioro. He put the 10 of spades in the first -- the early play indicated that he probably had that card. Jassem put the ace of diamonds in the second cage -- Jezioro had over-called at his first turn and his partner had contributed a small diamond without thought on the diamond play at trick two. When Jassem now played a heart and Jezioro played a small one, the third cage was filled -- it was a small heart.
There were no more cages in the North hand -- South had to have the queen of hearts. So Jessem took the heart king and finessed the 10 on the way back to score his slam. I congratulated my partner on his beautiful play, but I pointed out that he risked his contract by letting North lead a second spade at trick three -- what if the spades were 6-1? You are wrong, my dear friend, said Jessem, a la Sherlock Holmes. Take into consideration the vulnerability and that South passed initially. Any beginner with six spades to the queen-jack-10 in that kind of situation would have bid at least two spades, not one spade.