Double Dummy Corner

 

Competition Problem 87

composed by Steve Bloom
presented for solving in May, 2012

DR6

♠ 5

 KQ10

 K1032

♣ AJ875

♠ AKQJ1097

 32

 AQ7

♣ 10

♠ 86

 J84

 98

♣ KQ6432

♠ 432

 A9765

 J654

♣ 9

South to make four hearts against any defence.
What happens if the 8 and 9 are swapped?

Successful solver:  Jean-Marc Bihl, who suggested a DR of 5-6.  I found only one other solution in my e-mail in-box and that was incorrect.  As this is an all-time low for submitted solutions I have to wonder if some have gone astray, so please let me know if you submitted and haven't had a reply from me.  I'm honouring Jean-Marc's DR suggestion for now as the problem doesn't seem to me to be a DR7 or DR8, especially with the given hint concerning the heart pips.

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Solution

Ten tricks appear at first sight to be an easy target, with five heart tricks, three diamonds, the A a spade ruff, and a possible overtrick by setting up a second club trick for North via ruffing finesses after drawing West’s trumps.  However, South needing two entries for the diamond finesses and another for the spade ruff makes the play awkward, and in any case the defence can aim for a diamond ruff to take away one of these tricks.

First, suppose West makes the passive lead of a club or trump.  In that case declarer has some leeway in that the first three tricks can be won by any two trumps and the A.  A high club is covered and ruffed, followed by a diamond to the 10 and a second high club, also covered and ruffed.  West can capture the next diamond and give East a diamond ruff but after that the defence can take only one more trick, in spades.  A diamond lead (preferably the Q) leads to a similar result, North winning as cheaply as possible and leading a spade.  However, problems come to light when we consider spade leads.

A.      If West starts with a top spade, best defence is to continue the suit, threatening to lead a third spade when the lead is regained with the A, promoting a trump trick for East’s J.  The counter to this is to ruff the second spade, draw two rounds of trumps and then play A and another club—the J or 8—on which South throws the remaining spade loser.  Thanks to North’s 5 East is effectively endplayed: either red suit lead solves South’s entry problem for diamond leads and a club gives North an extra trick in that suit.

B.      So, what if West leads the 7 to East’s 8 so that diamonds can be attacked from East?  It is not at all obvious why that should make a difference, but it does.  As we shall see, it is now vital, after two rounds of trumps, for both North and South to retain a card higher than East’s.  Accordingly, North must run the 10.  After two rounds of trumps and the A, declarer plays as above but after the first club ruff the position is now like this:

♠ none

 Q

 K32

♣ 875

♠ AKQJ10

 none

 AQ

♣ none

♠ 6

 J

 9

♣ K643

♠ 43

 A9

 J65

♣ none

South must lead a diamond but now the defence can take the diamond ruff and lead a spade to force out North last entry in spades before the club trick has been established.  But that spade ruff isn’t North’s last entry if North’s last diamond is higher than South’s—and the only way to achieve that situation is for North to duck the third diamond!  Now we have a spade ruff, the 8 covered and ruffed, the A, a diamond to the K and the 7 takes the last trick.

Obviously the play in line B fails if South’s last trump isn’t higher than East’s, and that will be the case if East holds the 9 instead of the 8 and covers North’s 10.  Note carefully how it makes a difference for the first diamond to come from East, not West.  If West starts with the Q, for example, then play proceeds as before but now West cannot retain the lead when North plays low on the third diamond—either East ruffs it or South wins with the J.

A curious point arises.  The problem revolves around South’s need for entries to attack diamonds and yet the winning defence, after the heart swap, is for East to attack diamonds!

See the solution to Competition Problem #4 for the recommended tabular format if you prefer not to write in English prose.

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© Hugh Darwen, 2012

Date last modified: 11 March, 2017