Puzzle 8N67   Main

Deuce Trey Exchange

  by Richard Pavlicek

Are you tired of the Dow Jones Average? Looking for something better than Wall Street, or the New York Exchange? Of course you are, and you’ve come to the right place. Welcome to PavCo Street and the Deuce Trey Exchange! Trade with me, and your investments will reap high returns. As President and CEO, I assure you that I will do everything possible to prolong my pyramid, er puzzle scheme.

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).

Notrump S J 10 7 2 
S A 9 8 3Table S Q 5 4
N or S leads S K 6 

You start by leading the S 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 S 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 North-South to win an extra trick.

Layouts must fit the distributions below, with the deuce and trey originating in the hands shown. Fill in the remaining 11 cards (one per box) for each layout. Tab key will advance to the next box. North or South must always lead, whichever for best advantage, so assume adequate entries in another suit if needed for transportation. Play by both sides is with open cards.

Many solutions exist. Tiebreaking goals are (1) to win the most tricks, and (2) for the North hand to be as weak as possible, in that order of priority. Strength is judged by the sum of all card ranks: Ace = 14, king = 13, queen = 12, jack = 11, etc.

1. Notrump S  2
S  3 Table S
N or S leads S    

2. Notrump H  2
H Table H  3
N or S leads H    

To see if your solutions are successful click

Tina Denlee Wins

This puzzle contest, designated “January 2018” for reference, was open for over a year. Participants were limited to one attempt, unlike my usual contests allowing entries to be revised with only the latest one counting. Participation was fair, and there were 19 correct solutions. Tiebreakers were (1) for North-South to win the most tricks and (2) for the North holding to have to lowest rank sum, in that order of priority. Only three persons found the optimal solutions to both problems.

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).

Winner List
RankNameLocationTricks WonNorth Sum
1Tina DenleeQuebec460
2Jean-Christophe ClementFrance460
3Ryou NijiMichigan460
4Duncan BellEngland461
5Foster TomBritish Columbia461
6Martin VodickaSlovakia461
7Leif-Erik StabellZimbabwe462
8Dan GheorghiuBritish Columbia463
9Charles BlairIllinois464
10Sherman YuenSingapore464
11Samuel PahkMassachusetts464
12Joe LafortuneConnecticut361
13Tim BroekenNetherlands362
14Nicholas GreerEngland363
15Jim MundayMississippi364
16Radu VasilescuPennsylvania373
17Levi KatrielCalifornia258
18Jon GreimanIllinois259
19Jacco HopNetherlands265

Puzzle 8N67   MainTop   Deuce Trey Exchange


Part 1 (spade suit)

For the suit layout 4:4:3:2 (W:N:E:S) the deuce-trey exchange between North and West can produce two different trick changes: North-South winning 2 → 3, or North-South winning 3 → 4. For the first case, perhaps the most straightforward solution is:

NT win 2 S K J 9 2  NT win 3 S K J 9 3 
S Q 10 8 3Table S A 4 S Q 10 8 2Table S A 4
South leads S 7 6 5  South leadsS 7 6 5 

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:

NT win 3 S A J 6 2  NT win 4 S A J 6 3 
S K 10 5 3Table S 8 7 S K 10 5 2Table S 8 7
South leads S Q 9 4  South leadsS Q 9 4 

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].

Part 2 (heart suit)

For the suit layout 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:

NT win 1 H Q 9 8 2  NT win 2 H Q 9 8 3 
H 7 6 5Table H K J 10 3 H 7 6 5Table H K J 10 2
North leads H A 4  North leadsH A 4 

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:

NT win 1 H 10 9 6 2  NT win 2 H 10 9 6 3 
H 8 5 4Table H K Q J 3 H 8 5 4Table H K Q J 2
North leads H A 7  North leadsH A 7 

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.

Final Exchange

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!

Puzzle 8N67   MainTop   Deuce Trey Exchange

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