Competition Problem 130c
(found in Yarborough's collection, 1922)
South to lead at no-trumps. North-South to compel East-West to win four tricks in spite of their best attempts to avoid that fate.
Successful solvers: Well, only four people tried this one and nobody got it right (assuming my analysis is correct). Tables
I hope I've got this right! Let me know if you dispute any of these findings.
South leads the ♣Q, North playing low regardless of Westís play (why?ósee False Solutions, below).
A. If West (best) wins with the ♣K and returns the suit, North wins with the ♣A and advances the ♦7. East does best to discard a high spade. South discards the ♠6 and West does best to play the ♦5. With North to lead and North-South to lose three of the last four tricks the position is now:
North leads the ♦4.
1. If East discards a spade, South can let go of either seven. If the ♦4 wins, then
(a) If East discarded the ♠2, then North continues with the ♦2 to West's ♦Q.
(i) If East discards the ♠J, then South discards the ♠K West takes the last three tricks.
(ii) Otherwise, South's other seven goes away and East takes the last two tricks.
(b) If East discarded the ♠J, then South discards the ♠K on the ♦2 and West takes the last two.
Otherwise (West plays the ♦Q) South makes just the ♠K.
2. If East discards the ♥2, then South discards the ♣7. West does best to win and return a spade to Southís ♠K, but Northís ♣5 goes away and whoever wins the second spade wins the last trick too.
3. If East discards the ♣3, then South discards the ♥7. The situation is symmetrical to that in B, with Northís ♥J going away on the spades.
B. If West plays the ♣2 at trick one, South continues the suit, letting the ♣K hold. West does best to lead a spade but North discards the ♦7 and South plays the ♠6 under East's ♠Q (or the ♠3 under East's ♠2). If a second spade is led, then Northís ♦4 goes away as South wins, then North is entered on the ♣A to get out on the ♦2; otherwise, North gets the lead immediately and plays the ♦4 followed by the ♦2.
False solution 1:
In Line B, if North mistakenly plays the ♣A at trick one, we have this position:
C. If North leads the ♦7, East discards a high spade, South the ♥7 (as good as anything), and West plays the ♦5.
1. If North follows with the ♦4, West plays the ♦3 and East discards the ♠2!
(a) If North now leads a diamond, we have the following three-card ending with West on play and North-South requiring to lose the remainder:
West leads a spade on which North must discard the ♥J, but West then discards the ♣K on the winning ♥2 and South takes the last trick in clubs. (North would have won this trick instead if South had discarded clubs instead of spades on the diamonds.)
(b) If North leads a club, the three-card ending is similar except that North has the ♦2 instead of a club and South has ♠K63. West again exits on a spade and East has a loser in either the ♥2 or the ♣3 depending on Northís discard.
2. If North leads a club, we have the following four-card ending with West on lead:
West leads a spade and East plays the ♠2! South will have to win two tricks in the black suits however the spades are played.
D. If North leads the ♦2, East's simplest defence is to discard a heart (though a club discard also appears to work). West wins with the ♦Q and cashes the ♣K.
1. If South has no more clubs, then West plays the ♦5 and ♦3 to force North to win the last three tricks.
2. If South, having discarded a spade or a heart, holds a master club, West leads spade to Eastís ♠J. If the ♠J wins, East exits on a club and West discards a spade to force South to win the last two tricks in spades (or North with a heart and a diamond). If instead South wins with the ♠K and exits on the ♠3, East wins with the ♠Q and returns a club.
E. If North exits in clubs, West plays a spade to Eastís ♠Q. If South ducks the ending is as in C.2 except that West has the ♦5 instead of a spade and East is on lead. A club exit, on which West gets rid of a spade, leaves South having to win three of the last four tricks. If instead South wins the first spade we have
and North-South must take two more tricks, noting that East will win the next spade even if South leads the ♠3.
False solution 2:
Now, what if South starts with the ♠6, North throwing the ♥J? Then East lets the ♠6 win.
F. If South follows with the ♠3, then East wins and returns the suit, West discarding the ♦Q. West wins the next trick with the ♣K but can cash one diamond before exiting in clubs, such that North-South win the last two tricks.
G. If South leads a club, West wins with the ♣K and returns the ♣2. North does best to win with the ♣A and lead the ♦7 but East discards a spade and West wins and returns a spade. Eastís last two cards are the ♥2 and ♣4, both losing to South.
H. If South tries cashing the ♥7 and ♠K, West will win the first club with the ♣K to leave
East discards the ♠J on a diamond so that North-South take the last two tricks on Westís club exit.
False solution 3:
Next, what if North leads the the ♦2 instead of the ♦7 in line A. Here is the position with North leading the ♦2:
East must discard the ♥2! West wins with the ♦Q. Now:
I. If South has discarded the ♠K, West leads the ♠5. East wins and exits to South on a club, West discarding the ♠4. North-South win the last two tricks because East can get under the ♠3 and West can get under the ♦4.
J. If South has discarded the ♠6, wins the spade continuation with the ♠K, and exits on the ♠3, East wins and gets out on a club.
K. If South has kept three spades and a club and wins the spade continuation, East can win the next spade and exit in clubs.
L. If South has kept three spades and a club and lets East win a spade, East exits immediately in clubs and West jettisons the ♠4.
M. If South has kept three spades and a heart, West leads the ♦5, which wins, and then the ♦3 to give North the last three tricks.
False solution 4:
Finally, if South starts with a low club instead of the ♣K, West plays low. Now if North wins with the ♣A the position is equivalent to when the ♣Q is led at trick one, whereas if North plays low East can win with the ♣10 and return a heart on which West discards the ♣K.
See the solution to Competition Problem #4 for the recommended tabular format if you prefer not to write in English prose.
Hugh Darwen, 2015