## Solution to the Grand Slam Problem

Here's the Bridge problem repeated for convenience:

```

A K 7 6 5 4 3
3 2
A K 2
3
Q J T 9 8                    2
4                            Q T 8 7
Q J T 9                      8 7 6
K T 2                        8 7 6 5 4
-
A K J 9 6 5
5 4 3
A Q J 9

```
West leads the Spade Queen against your contract of Seven Hearts. How do you play to win all the tricks?

A grand trump coup is sufficiently rare that it is often the highlight of a bridge session when it occurs, although it isn't difficult or exotic enough, by itself, to constitute a good bridge puzzle. The same statements would apply to a repeating triple squeeze.

We would certainly not expect these two unusual themes, trump coup and triple squeeze, to apply in the same bridge hand. When a trump coup arises, trumps are the only problem suit; in fact in a ``grand'' troup coup you have extra side winners you end up ruffing. In a repeating triple squeeze, the trumps are solid, there are contested tricks in all three of the other suits, and you are two winners short of your contract. Yet this play problem combines the ideas of Grand Trump Coup and Triple Squeeze! (``Grand'' coup means a winner is ruffed -- here the winner is ruffed at Trick Two!)

The successful play is to win the opening lead in dummy, discarding a diamond from the closed hand, and lead the remaining spade honor. It won't do any good for East to trump this, so we assume he discards either a diamond or a club. (In fact he's faced with a ``Hobson's Choice:'' he wants to discard diamonds so he can trump later when declarer uses dummy's diamond honors as entries for a trump coup, but he needs to keep his Diamond Eight guarded to prevent his partner from being squeezed.)

If East discards a diamond at trick two, dummy's Deuce becomes a threat against West and a triple squeeze will operate. Discard a club on the spade winner, finesse a heart, cross to Diamond Ace, finesse another heart, play off all the trumps pitching spades from dummy, and cross to Diamond King for a 3-card ending. West will be very squeezed. He must keep King and another club, so he doesn't have room to protect both spades and diamonds. Cash dummy's winner and West is squeezed again.

If East discards a club at trick two, he retains a diamond guard and West can no longer be squeezed, but another play operates. Trump your winning spade at Trick Two! Play Ace of Clubs, then more high clubs, ruffing West's King when it appears. Finesse in hearts, cash the remaining clubs, cross to Diamond Ace, trump a spade, cross to Diamond King, trump a spade, take the final tricks with high trumps. This line won't work if East discards a diamond at trick two: he'll throw another diamond on another spade and later trump your Diamond King.

I saw this hand presented in the puzzle section of Technology Review. I changed it slightly, reversing Spades and Clubs. Since the simple-minded double dummy solver always tries spades first, it will find the winning play (a spade lead at trick 2) in about 1 minute. The other way, it would take about 2 minutes. The players' holdings contain many ``straight flushes'' (like West's Q J T 9 8 of Spades) where the software will treat the cards as equivalent -- otherwise solution would take much longer.

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