## Problem no. 24, 2005

### The problem

Paul Lukacs lived between 1915 and 1982. He represented Israel i international competition, but above all is he known as a skilled constructor of instructive bridge problems.
Our new problem consists of three similar declarer play problems, all of them from Paul Lukacs. Your task is to find the best plan on each of them. In all problems, the bidding went like this:

 South West North Esst 3 3 4 6 pass pass pass

North-South use standard leads and signals. On all of the problems, North leads the king of spades. Dummy wins the trick with the ace, and South plays the deuce. When declarer leads a trump to his ace, North discards a spade.
How should West continue to maximize his chances to make his contract in each case? I need three answers, but it is possible that two of them (or all three) are the same.

1)

 6 3 A 5 K Q 8 7 A 4 3 2 A Q 5 4 3 K J 7 6 2 A 8 K 7

2)

 6 3 A 5 A 4 3 2 K Q 8 7 A Q 5 4 3 K J 7 6 2 A 8 K 7

3)

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

### Solution

The bidding and the two first tricks have been very revealing. South has at least seven clubs and precisely three diamonds; North has no diamonds and at least seven spades. Since the defenders use normal signals, South can't have a doubleton spade (then, he would have played his highest spade to the first trick, to show an even number of spades). Therefore, we can assume that spades are 8-1.
If hearts are 3-2, you have no problems, so the only danger is that North has four (or five) hearts. But that is only possible if South has at least eight clubs. If he only has seven, hearts have to be 3-2.
In problem No. 1, this is the lay-out you should cater to:

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

When North doesn't follow to the first trump round, you lead a trump to the king and check the club position by cashing ace and king. If North follows twice, all is well, as hearts are almost guaranteed to be breaking. Then you draw the last trump, cash the heart king and exit in spades. You will make you slam not only if hearts are 3-2, but also if North has the distribution 7-4-0-2 (but if he has, South has played a false card to the opening lead) and South has one of the three top hearts (the jack, ten or nine). If South wins the spade trick, he has to give a ruff and sluff; if North wins the spade trick, he can't exit in hearts without giving up his trick in that suit.
If clubs are 8-1, there is an even better plan, which lands the slam even if North has J-10-9-x in hearts. If West cashes the heart king and exits with a low trump, he loses an unnecassary trump trick to South, but that trick comes back on the forced club lead, against the double void, and then there will be a squeeze against North in the majors. West ruffs South's club lead in dummy and plays out his last trumps, forcing North to surrender:

 Q J 10 – – 6 5 8 A 4 4 – – – – – – Q J 10

When the four of diamonds is played, North needs all his cards, but he must part with one of them.

In problem No. 2 you can follow this plan exactly, of course, but since you have two heart honors in dummy, there is an even simpler plan available. Draw trumps (and keep at least one trump entry to West), cash ace and king of clubs. If North only follows once, exit in spades. If South wins the trick, his distribution was 2-0-3-8; he is endplayed. If North wins the trick, he is endplayed – and since you know he has at lest four hearts, you will pick up the suit without loss: just play a small card from dummy on the heart return and then take a double finesse over North.