## Problem no. 23, 2005

### The problem

Our new problem comes from Richard Pavlicek from The United States. It's about the "optimum contract", an expression which refers to the highest scoring contract one side can make against best defense.

 9 J 10 9 A Q 4 3 2 A K Q 2 – A K Q 8 – A K Q 8 7 J 10 9 8 7 6 5 K 8 7 6 5 4 3 J 10 9 J 10 7 6 5 4 3 2 6 5 4 3 2 – –

There are two questions to this problem.

1. What is the optimum contract for North-South?
2. What is the optimum contract for East-West?

### Solution

I asked for two bids, but one is enough. Both sides' optimum contract happens to be 3 spades.
North-South can make their contract if South is declarer. He wins the first four tricks in dummy with the diamond ace and the three club honors. When he then plays the queen of diamonds, the defenders can only get four tricks, no matter if East discards or ruffs low (if he ruffs high, declarer makes an overtrick).
East-West make their contract if East is declarer. Then, East can win the first six tricks with one trump and five hearts. When he exits in a minor, South is forced to ruff and lead trumps, so that East makes three more trump tricks.
As one of our solvers writes, this is the highest suit contract which both sides can make. In notrump it is trivial to construct deals where both sides make a grand slam, for instance when South has twelve solid spades and the ace of hearts, and West the remaining major suit cards, while the minor suits are distributed in the same way between North and East (so that East has thirteen winners). Then both South and West can make 7 notrump.

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