Puzzle 7F24   Main

# Lucky Sevens

by Richard Pavlicek

Somebody probably should have bid 3 NT — though no bargain, it surely has a better chance than this contract.

 5 SouthNone Vul J 3 2 Q J A K 7 2 Q 7 3 2 WestPassPassAll Pass NORTH1 3 4 EastPassPassPass South2 3 5 ?  ?  ?  ? ?  ?  ?  ? Lead: 10 A K 7 7 3 2 J 8 A J 9 8 6

Against 5 West leads the 10 and South can make his contract. Curiously, if any seven were switched with the six (of the same suit), South could be defeated. What are the exact East-West hands?

Oh, yes, I have to tell you that East has the A.

## Solution

At first glance it seems that none of the sevens can be significant, but let’s look closer. Consider the 7. For it to be significant, a probable layout is that East holds the protected queen and the six-spot, which allows declarer to transfer the sole spade guard to West by covering the 10 with the jack (or by leading the jack later). If the 7 and 6 were switched, this transfer would not be possible.

Now consider the diamond suit: North’s 7 would be a natural trick if East held 10-9 doubleton (South runs the jack) so this may be the diamond layout.

For the relationship of the 7 and 6 to be significant, the former must be a key entry to dummy. This seems unlikely with the Q in dummy, so it must be necessary to spend the queen early in finessing — which suggests West may have the singleton 10.

But what about the heart seven? This is the most difficult to imagine, but it might come into significance in a bizarre squeeze scenario if one player held 10-9-8.

Consider this construction:

 5 South J 3 2 Q J A K 7 2 Q 7 3 2 Trick1 W2 S3 S4 N5 N6 S7 S8 W Lead 10 J 8 Q 2 A 2 9 2nd23445 5KJ! 3rd62K8J3JQ 4thK91010 8K4A W-LW1W2W3W4W5W6L1W7 10 9 8 K 10 9 8 Q 6 5 4 3 10 Q 6 5 4 A 6 5 4 10 9 K 5 4 Lead: 10 A K 7 7 3 2 J 8 A J 9 8 6

The 10 is won by the king (optionally, declarer could cover in dummy). South leads the J, ducked (best defense to limit declarer’s entries to dummy) then a diamond is led to the king. The  Q is led (East ducks and South unblocks the eight), then trumps are drawn with another finesse. South leads a heart, which West must win to continue spades; jack, queen, ace. This leaves the following ending:

 win 4Success 3 Q A 7 7 Trick9 S10 N11 N Lead 6! A Q 2nd 9 5A 3rd7 73 4th 4610 W-LW1W2L1 8 10 9 Q 6 — 5 4 A 6 5 — — South leads 7 7 3 — 9 6

On the 6 West is squeezed in three suits. Note the power of the 7! If West lets go another heart, the 7 can be established by force after South discards his spade loser on the A.

Observe that this squeeze would not work if East held the 7 (and South the 6), nor if East held the 7 (and South the 6). If the 7 were switched with the 6, West could defeat the contract simply by cover the J. And don’t forget that 7 entry to dummy.

 Puzzle 7F24   Main Top   Lucky Sevens