Puzzle 8S13   Main

Diamond Stack

  by Richard Pavlicek

With my new-found wealth in space travel, I have reopened the Jwaneng mine. PavCo Diamonds is back in production! Our catalog features 50 new creations, like the breakfast cereal bowl pictured above, and a diamond studded hat rack with an ivory base. Low overhead, courtesy of PavCo Cayman Bank, means unbeatable prices! PavCo Diamonds should put De Beers out of business in a month (five weeks tops) as its customers flock to our offshore warehouse. The diamond craze also inspired a bridge curiosity, which I will present as a puzzle.

How many times have you found a suit stacked behind you, either as trumps or a side suit that cannot be established? Witness the egregious diamond stack on the following deal, which not only renders an excellent grand impossible but jeopardizes six as well.

6 NT South S A 5 4 3
H A K 6 5 4
D 2
C A Q 4
Both Vul   West

All Pass
1 H
2 S
4 NT
2 D
3 NT
6 NT
S J 10
H 9 8
D 10 8 7 6 5 4
C J 9 5
Table S Q 9 8 7 6
H Q J 10 7
C 10 8 7 6
Lead: S J S K 2
H 3 2
D A K Q J 9 3
C K 3 2

After winning the S A in dummy, declarer leads a diamond for what appears to be an early claimer. Oops! East’s discard changes that picture. Diamonds cannot be established, but declarer can still succeed by elimination technique. Many sequences will suffice, but best is to cash three top diamonds, H A-K, C A-Q, C K and S K; then exit with a low diamond, endplaying West. This would also work if West had three spades and two clubs, as the C K would force a spade pitch lest diamonds be established.

Given the D 2 in North, South’s D A-K-Q-J-9-3 (rank sum 62) is the weakest possible holding to succeed against the 6-0 break offside. If any card is reduced, say D A-K-Q-10-9-3 or D A-K-Q-J-8-3, South fails. Of course D K-Q-J-10-9-8 would also succeed, but that’s stronger (sum 63). Note that D K-Q-J-10-9-7 (sum 62) would fail, even if not led until six cards remain, as West holds up his ace four times.

In the above scenario declarer needed five diamond tricks. More often he will need fewer, which introduces this three-part puzzle:

With a 6-6 suit division, what are the minimal holdings to win (A) four, (B) three and (C) two tricks?

Enter South’s diamond holding (any six cards excluding the D 2) to win the number of tricks required (West will get what remains). Assume diamonds will not be played until six cards remain, and South must lead first. To succeed, South’s holding in each part must be within one pip of minimal. Successful solvers will be ranked by the sum of all South cards (lowest is better); and to celebrate the fall of De Beers, ties will be broken by the most South beer cards. I’ll drink to that!

Win 4 tricks    South  D
Win 3 tricksSouth  D
C.Win 2 tricksSouth  D

To see if your solutions are successful click

Andrew Spooner Wins

This puzzle contest, designated “July 2018” for reference, was open for over a year. Participants were limited to one try, unlike my usual contests allowing entries to be revised with only the latest one counting. Participation was mediocre (an overbid) no doubt because it was less fun than my previous two novelty puzzles. There were 11 correct solutions, of which five were optimal.

Congratulations to Andrew Spooner, who was the first to submit the perfect solution. Andrew is a more recent participant, with a number of high finishes, and the winner of my Unusual Hands puzzle last year.

Ranking is by the least sum of the three South holdings, most beers (use of D 7) and date-time of entry, in that order of priority.

Winner List
RankNameLocationSouth SumBeers
1Andrew SpoonerAustralia1402
2Tim BroekenNetherlands1402
3Jean-Christophe ClementFrance1402
4David WuCalifornia1402
5Samuel PahkMassachusetts1402
6Duncan BellEngland1401
7Gareth BirdsallEngland1400
8Nicholas GreerPennsylvania1412
9Dan GheorghiuBritish Columbia1412
10Radu VasilescuPennsylvania1410
11Levi KatrielCalifornia1422

Puzzle 8S13   MainTop   Diamond Stack


Part A

The weakest South holding to win four tricks has a rank sum of 54:

D win 4 D
D Q 10 8 7 6 5Table D
South leads D A K J 9 4 3 

Samuel Pahk: I just can’t get the beer card into a 54 sum, no matter how long I work on it.

Too many beers can ruin a bridge game, so I did my part to keep you sober.

Part B

The weakest South holding to win three tricks has a rank sum of 46 — and a beer:

D win 3 D
D K Q 10 9 8 4Table D
South leads D A J 7 6 5 3 


Ninety-nine bottles of beer on the wall;
Ninety-nine bottles of beer.
If one of those bottles should happen to fall,
It could land on this page if it landed at all.

Part C

The weakest South holding to win two tricks has a rank sum of 40 — and another beer:

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

Oh no! The beers outnumber the non-beers! In order to prove that bridge is a fair game, I should point out that the weakest holding to win one trick is D 9-8-6-5-4-3. Look, mom! No beer!

Crash-out Time

Anonymous: I didn’t enter this contest because my computer crashed, or maybe it was just me after the party last night. No, wait… It was my car, and the friggin’ hospital has no Internet.

David Wu: Bridge is too hard. Just get bashed!

Puzzle 8S13   MainTop   Diamond Stack

© 2021 PavCo Diamonds, Inc.
elegant solutions for the filthy rich