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As declarer in notrump, suppose you need two tricks from the spade suit below. At the table, of course, you wouldn’t see the East-West cards, but at PavCo we reveal everything (except our ledger books).
You start by leading the J from dummy, which East (also seeing all) covers, lest his queen later fall on air; king, ace. West exits safely in another suit, then you next lead the 6; eight, 10. Only dummy can lead now, and its remaining 7-2 cannot win a trick against West’s 9-3; hence you fail, winning just one trick. (Starting with low to the king would also fail.)
This brings me to the puzzle scheme: If you exchange the deuce and trey, an extra trick can be won. The play would be the same, but North would remain with 7-3 against West’s 9-2, then the lead of the seven squashes East’s five to establish the three.
This phenomenon — altering a suit’s trick outcome by swapping its deuce and trey — can occur only when the hands with the deuce and trey have 4+ cards each and are on different sides. That is, it cannot occur between partnership hands. Now it’s your turn!
Create two suit layouts where exchanging the deuce and trey allows declarer to win an extra trick.
Distributions must fit Layouts 1 and 2 below, with the deuce and trey located as shown. North or South must always lead (from either hand to best advantage) with double-dummy play all-around. Further, assume adequate entries in another suit if needed for transportation.
Multiple solutions exist, so a further goal (tiebreaker) is to win the most tricks, and secondarily for the North hand to be as weak as possible (judged by the sum of its card ranks). Before reading the solutions, try it yourself or make your best guesses.
1. Which spade suit (WNES order) is the winner?
2. Which heart suit (WNES order) is the winner?
Quit
Congratulations to Tina Denlee, Quebec, who was the first to submit the optimal solutions. Tina is a long-time participant, finishing high almost every time entered, and the winner of Fewest HCP Notrump in 2016. But to me, Tina is most appreciated for her many insightful comments, not only in technical merit but with a dry sense of humor.
Ranking is by tricks won and North sum before the swap. Optimal for Problem 1 is 3:33, and Problem 2 is 1:27, so a perfect total is 4:60. Further ties are broken by date and time of submission (earliest wins).
For the suit distribution 4:4:3:2 (W:N:E:S) the deuce-trey exchange between North and West can produce two different trick changes: Declarer winning 2 → 3, or declarer winning 3 → 4. For the first case, perhaps the most straightforward solution is:
Jacco Hop: Probably far from optimal, but hey, at least it’s a correct solution!
Indeed it is. As long as West covers every card South leads, only two tricks can be won. But if the deuce and trey are exchanged, North-South can win three tricks.
Because my main tiebreaker was for N-S to win the most tricks, the second case was necessary to rank high. Many possibilities exist, but one stands alone to give North the lowest possible pip count (33). The optimal solution:
Ryou Niji: Only three tricks can be won, but with the deuce-trey swapped, North-South can win all four provided South leads three times [saving the four-spot until last].
For the suit distribution 3:4:4:2 (W:N:E:S) the deuce-trey exchange between North and East can produced two different trick changes: North-South winning 0 → 1, or North-South winning 1 → 2. The latter of course is desirable for my tiebreaker. One successful attempt:
Charles Blair: North-South can win only one trick, but the deuce-trey swap allows a second trick to be established. A similar layout with the heading “A Three Wins by Weight” appears in Right Through the Pack by Robert Darvas.
The previous North holding has a pip count of 31. The optimal solution reduces it to 27 with this unique layout:
Ryou Niji: Only one trick can be won, but the deuce-trey exchange allows the 10 to be led (covered jack, ace) then the seven (covered eight, nine, queen) and finally the six to force the king and squash the five.
Tina Denlee: The Deuce Trey Exchange is like the Stock Exchange: The truth is hidden deep beneath the surface.
Jim Munday: I’m usually better at losing tricks, but I gave it a shot.
Duncan Bell: I’m guessing my solutions aren’t optimal but the best I can come up with before bed.
Foster Tom: I’m happy to see your puzzles still running!
Dan Gheorghiu: Thank you, Professor, for reminding me. I wouldn’t miss your puzzles for anything in the world!
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by Richard Pavlicek by Richard Pavlicek