## Problem No. 3, 2000

### The problem

A couple of years ago, my good old friend Björn Sanzén moved to Lund to study at the university. On a couple of occassions he played as an excellent substitute on our team in the local league, usually as my partner.
In one of the matches, he was declarer in 2 notrump after all four players at the table had bid something. The contract was normal, the opening lead was made, and I tabled the dummy. Björn won nine tricks, when he against best defense would have made only eight. But the fun thing about the deal was that before the first trick was played, Björn know both opponents' distributions!

### Solution

The full deal was (dealer North, neither side vulnerable):

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

 South West North East pass 1 D 1 2 pass 2 NT pass pass pass

West led a low spade, dummy played the nine – and when East discarded to that trick, Björn knew both opponents' distributions! What's more: it was very easy.
When East didn't have a single spade, he had to have at least five cards in one or more of the other suits. And the only distribution he could have is 0-4-4-5.
He did open with 1, so his longest suit has to be clubs, at least five cards long. And since Björn and I had eight clubs together, East had to have exactly five. And he can't have another five-card suit, because with 5-5 distribution he would have opened with his higher suit. Therefore, his eight red cards has to be distributed 4-4.

The lay-out doesn't have to be exactly this one, of course, but the two important points in the reasoning is tha (a) East doesn't follow to the first trick, and (b) North-South have eight cards in hisopening suit. Therefore, we know he has exactly five cards in his opening suit. And when the opening bid was 1, 0-4-4-5 is his only possible distribution.
There is an alternative solution, in which East opens with 1 and later is void in spades. If North-South have eight diamonds and nine clubs together, South knows East must be 0-4-5-4. If they have fewer than nine clubs, it's possible that East is 0-3-5-5, so in that scenario South can't be sure. But it's highly unlikely you'll end in 2 notrump with eight diamonds and nine clubs together, and it's difficult to construct a realistic deal from these conditions. But if the opening bid is 1, the rest is easy.

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