The Thirteenth Trick

There are twelve tricks for North/South in any denomination.

The only grand slam which makes, however, is 7 ♦.

The key is to try to engineer a heart ruff in North, and the strain this plays on West's hand.

On a non-diamond lead (say a heart,) declarer cashes two clubs, and then plays four rounds of spades, leading to this position on the fourth spade, with West to play:

If West ruffs, North overruffs, ruffs a club in South, then draws trumps and claims, with the heart entry available to play a club winner.

If West pitches a heart, he gives up a trick in that suit. Declarer just draws trumps and claims.

If West pitches a club, North pitches a heart, a heart to North's king, then a club ruff with the eight, which West cannot overruff. He must either pitch the good heart, or underruff. Neither matters - a heart is ruffed in North and South has only high trumps.

On a diamond lead, the end position is reduced:

West is stuck in the same dilemma on the ♠ Q lead.

The issue of the heart honors is actually unnecessary. The same position switching the hearts nine and ten:

If West pitches a heart here, North pitches a heart, scores the heart king, ruffs a club in South, then ruffs a heart. South remains with just the two high diamonds.