Double Dummy Corner

Competition Problem 107a

composed by Ian Budden
presented for solving in January, 2014

 DR5 ♠ K43 ♥ Kx5 ♦ Q6 ♣ 76543 ♠ A98765 ♥ 9 ♦ J10 ♣ J1098 ♠ QJ10 ♥ Qx76 ♦ K987 ♣ KQ ♠ 2 ♥ A8432 ♦ A5432 ♣ A2

The contract is four hearts by South. West leads the J.

The cards marked x are the J and 10.
Which of the following statements is true?

A. The contract succeeds regardless of the position of the J and 10.
B. The contract fails regardless of the position of the J and 10.
C. The contract succeeds only if North holds the 10.
D. The contract succeeds only if North holds the J.

Show how the contract succeeds or fails in each case.

Successful solvers:  Jean-Marc Bihl, Steve Bloom, Radu Mihai, Sebastian Nowacki.   Tables.

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Solution

Statement D is correct.

1.       North holds the J.  The J lead is covered by the Q, K, and A.  South leads the ♠2.

A.      West wins and leads a club (best).  South wins, crosses to the K, cashes the ♠K for a club discard, and exits with a diamond.  Declarer ruffs the black suit return, ruffs a diamond, ruffs the other black suit, ruffs a diamond, and leads a club from dummy.  East is endplayed.  If he ruffs low, South overruffs and still has the A;  if instead East ruffs high, South discards his diamond and East has to lead into the trump tenace.

B.      West ducks.  North wins with the ♠K and leads another spade on which South discards the ♣2.  The defence lead another spade.  South ruffs and exits with a diamond to West.  West returns:

i.        the 9 (a club amounts to the same thing).  North wins with the K, crosses to the ♣A, ruffs a diamond, and play continues as in line A.

ii.       a spade.  North discards a club and East a diamond.  Declarer ruffs, cashes the ♣A, ruffs a diamond low (or overruffs with the J if West ruffs in), ruffs a club, and leads another diamond.  If West ruffs this diamond or the previous one, North plays the K and leads a club for the endplay as in line A.  If instead West still has the 9 and discards two clubs on the diamonds, North discards a club also, and East wins.  North wins the heart return as cheaply as possible, and declarer makes the last two tricks on a high cross-ruff.  (If West discards a spade and a club, or two spades, on the diamonds, either option works.)

2.       North holds the 10.  The J lead is covered by the Q, K, and A.  South leads the ♠2.  To defeat the contract the defence must follow line B(ii) above.  East must discard a diamond on the fourth spade, and West must discard a club when South leads a diamond to ruff in dummy.  With four cards left the position is

 ♠ none ♥ K10 ♦ none ♣ 76 ♠ A9 ♥ 9 ♦ none ♣ J ♠ none ♥ QJ76 ♦ none ♣ none ♠ none ♥ A8 ♦ 54 ♣ none

When South leads a diamond, West must discard the master club.  Now, whether North discards or ruffs high, the defence will come to two more tricks.  If instead West ruffs or discards a spade, North overruffs or ruffs with the K and East is endplayed on the lead of a club.

South will be able to manoeuvre to reach the position needed for the successful endplay if either: