100%

by Paul Lukacs, with Ted Muller

South leads the ♠Q.
East to make 6♠ against any defense and distribution.

When first published, this problem was touted as being only 99.9% secure, which means that the author missed the hand's best feature (in failing to appreciate that the diamond situation was immaterial).  A truly elegant layout, this is a composer's dream in that there must be no variation in the sequence of plays.

Declarer wins the ♠A; in order for there to be any problem, trumps must split 3-0.  Assuming that to be the case, the ♦A is led.  If that is not ruffed, a spade is played to the king, then a club toward dummy.  If south is void, he cannot afford to ruff a loser.  The ♣K wins, and a heart is played to the ace.  If that is ruffed, then the club loser goes away on the ♦K and a marked heart finesse is taken.

If the ♥A wins, another club is led toward the ace.  Now a club is discarded on the ♦K.  If that is not ruffed, south is thrown in with a spade, and he is endplayed.  Declarer covers a lesser club lead, or gets a free heart finesse.

If, at trick two, south does ruff the first diamond and returns a black suit, declarer wins the ♠K and ♣K, then plays off two high hearts.  If north shows out on the first heart, then his pattern must be 0-0-10-3; after discarding a club on the other diamond, a club ruff will set up a trick for a heart discard.  Alternatively, if north shows out on the second heart, then he is 0-1-10-2; the trumps are drawn, squeezing south in clubs and hearts.  Finally, if north follows to two heart leads, then he can have only one club, and a second-round finesse in that suit is marked.