## Problem no. 2, 2000

### The problem

Our good friend Max Ödlund, of Stockholm, Sweden, once told us this amusing problem. Let's see if you can solve it!

Back in 1975 it was popular to go to London and play rubber bridge at one of the rubber bridge clubs there. So when a friend of yours says there are cheap flights to London, you buy one, hoping to make a little money by playing bridge. But things don't go as expected, and before the last day you have lost money, quite a lot. But there's still time for one last rubber, before the bus takes you to the airport – and now everything goes your way. Yes, the opponents make a game on the third deal, but that is quickly compensated by the 500 and 800 you collect in doubled undertricks on the two following deals. But time is running out, and if want to return to Sweden, the next deal has to be the last on. A quick glance at the protocol, compared with your previous results in the week, says you are exactly 1000 points down. But the last deal doesn't take long. And what's more: you score a game, ending the rubber in he normal way, and win exactly 1000 points on the deal.

### Solution

There is one important clue, which is easy to miss: that you played rubber bridge.
In tournament bridge you score points in two ways: by making a contract or by defeating the opponents' contract. In rubber bridge there's a third way: you can score for honors too. In a trump contract, the honors are ace, king, queen, jack and ten in the trump suit; in notrump they are the four aces.
You also know that the rubber was ended, so you must have bid and made a game. Furthermore, you won 1000 points on the deal. But if you try and count on various contracts, you'll find that you never got those 1000 points. Therefore, the honors have to be involved. And they surely are!
This is what happened: On the last deal you and your partner bid 3 notrump. One of your opponents had the four aces, so he took a chance and doubled. Three passes followed. Soon it became obvious to you that the contract couldn't be defeated, but the defender didn't know that, and when you had knocked out two of his aces, he didn't cash his remaining aces (desperately hoping for a miracle), so you took the rest. For 3 notrump doubled making five you got 200 for the tricks, 50 for making a doubled contract and 400 for the overtricks. And since both sides were vulnerable, you got 500 for the game. All in all 1150 points.
And then we had the honors. The four aces in one hand gave the opponents 150 points. And the difference between 1150 and 150 is exactly 1000 points.

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