Main     Puzzle 8M07 by Richard Pavlicek    

The Case of the Four Aces

“Come, Watson, come! The game is afoot. Inspector Lestrade seeks our aid to build a case against a conniving perpetrator from across the pond. To set the stage suppose you hold S 5 H K-Q-J-10-5-4 D J-6-5-4 C K-5.”

“I say, Holmes, a perfect hand! Twenty-nine points with the right jack, but I have too many cards.”

“Not cribbage, you bumbling quack; bridge. North on your left opens a spade, which by foreign convention shows five, and South bids two notrump showing a balanced hand of 12 to 14 high-card points. Your side is vulnerable. What would you do?”

“Can I meld my heart sequence and four fives?”

“I think not. You know my methods, Watson. I would pass, because I have a promising lead and a vulnerable three-heart bid is risky. North raises to three notrump, which ends the auction. What would you lead?”

“Ah! Now I remember bridge! In my youth I penned a book on it, Play of the Hand. Wait a minute, I’ll fetch it and look it up… [thumbing to page 165]. Here it is, fourth best… ten of hearts!”

g/holmes4.gif
3 NT South  ?
 ?
 ?
 ?
E-W Vul

West

Pass


North
1 S
3 NT


East
Pass
All Pass


South
2 NT
S 5
H K Q J 10 5 4
D J 6 5 4
C K 5
Table S Q J 10 9 6
H 6
D K 9 3
C 9 8 6 2
Lead: H K  ?
 ?
 ?
 ?

“[Sigh] Close enough. According to Lestrade, the East-West players claimed that South played as if he could see through the backs of the cards, winning nine tricks against best defense, and remarkably spending four aces on the first four tricks. If we could fathom his course of play, it could be crucial evidence. This hotshot yankee declarer must be held accountable to the Crown’s justice.”

“I’m sorry, Holmes. I don’t see any North-South cards.”

“Would it matter if you did? Never mind. That’s all the information Lestrade has. After filing their charges, the East-West players are mysteriously missing and feared dead. South has lawyered up and won’t speak to anyone, and North conveniently swears he remembers nothing. The court will need more evidence for a conviction. I cannot give it my full attention because of the Moriarty kidnapping, and you’re obviously hopeless. Wait! I’ll ask Pavlicek to put it on his web site.”

Always happy to assist Scotland Yard!

Construct a North-South layout consistent with the facts of the case.

A further goal is to have the most aces (tricks 1-4) won out of necessity (i.e., another option will not suffice). Give it a try before reading the best solutions below.

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Dan Gheorghiu Wins!

In May 2015 this puzzle was presented as a challenge, inviting anyone who wished to submit a solution. Only 19 people were brave enough to give it a try, of which the 12 listed below constructed a layout to fit the conditions, and where South can make 3 NT against any defense after the H K lead. Thanks to all who participated, though “all” may be an overbid.

Congratulations to Dan Gheorghiu, British Columbia, who was the only solver to submit the maximal solution for necessity* and equalize the N-S totals. (Charles Blair got the hard part but was off a few points in the totals.) Dan is a new participant this year and he’s been on a tear: eighth in February, fourth in March, third in April, and now first in May. That’s the good news! The bad news is that he may be out for June, having to testify for Scotland Yard.

RankNameLocationNecessity*NorthSouth
1Dan GheorghiuBritish Columbia7104104
2Charles BlairIllinois7102106
3Julien ReichertFrance5104104
4Nicholas GreerEngland4104104
5Jamie PearsonOntario3104104
6Adam DickinsonScotland3104104
7Jon GreimanIllinois3104104
8Grant PeacockMaryland3104104
9Tim BroekenNetherlands2104104
10Jacco HopNetherlands2100108
11Jim MundayMississippi1104104
12Christina SyrakopoulouGreece193115

*Maximum is 7, scored as follows: One point if winning the first trick is necessary. At tricks 2-4, one point if necessary to lead the chosen suit, and one point if necessary to play the ace. Also, the defense cannot deprive you of winning an ace by making an alternate play that doesn’t gain. For example, if South leads a club and North has the ace, West will play the king unless playing low would gain a trick for the defense.

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Solution

After winning the H A, it is almost mandatory to keep West off lead, so the C A should be in dummy behind West’s king. Further, there’s no reason why South can’t have five clubs in his required balanced hand. This leads to a straightforward solution:

3 NT S K 8 7 4 3
H A 8 7
D 10 7 2
C A 7
Leader
1. W
2. N
3. S
4. N
Lead
H K
S 3
C Q
D 10
2nd
A
6
K
K
3rd
6
A
A
A
4th
2
5
2
4
S 5
H K Q J 10 5 4
D J 6 5 4
C K 5
Table S Q J 10 9 6
H 6
D K 9 3
C 9 8 6 2
S A 2
H 9 3 2
D A Q 8
C Q J 10 4 3

Jon Grieman: [At Trick 2, lead a spade] to the ace; C Q covered and won; D 10 covered and won. Clubs are then established to provide a ninth trick with the D Q entry. I’m pretty sure this counts as zero aces out of necessity, although once the suit is led, ducking would certainly be hazardous to the contract.

Jon was a little pessimistic, as he scores 3 on my necessity scale. It was necessary to win the S A, C A and D A after the suit was started. Points were lost because Trick 1 could have been ducked, and a different suit could have been led at Tricks 2-4. The play, however, would certainly arouse suspicion with declarer grabbing the first trick as if he knew hearts were 6-1. “How con-veen-ient,” said the Church Lady.

Julienne cut French fries

Our French connection took no chance of losing the first necessity point with this solution, as only a revoke could prevent winning Trick 1. The layout embraces most of the intended puzzle theme.

g/holmes4.gif
3 NT S K 7 4 3 2
H A
D 10 8 7
C A J 7 4
Leader
1. W
2. N
3. S
4. S
Lead
H K
S 2
D A
C Q
2nd
A
9
4
K
3rd
6
A
7
A
4th
2
5
3
2
S 5
H K Q J 10 5 4
D J 6 5 4
C K 5
Table S Q J 10 9 6
H 6
D K 9 3
C 9 8 6 2
S A 8
H 9 8 7 3 2
D A Q 2
C Q 10 3

Julien Reicher: At Trick 2 a low spade must be led, and even if playing the six does not cost a trick, I will assume East splits to force the ace. After that, a high heart can still enable nine tricks; but the only other option is the D A, then a high club (or the last spade first but it’s not what I want), covered by West (normal play) and necessarily won. Then a diamond from dummy kills East, giving me nine tricks (three clubs, two diamonds, one heart and three spades after a throw-in).

Julien’s analysis is spot on, losing a point as noted for the optional high heart at Trick 3 and another for the optional spade at Trick 4. Still, 5 out of 7 necessity points topped all but two solvers. North and South totals are perfect at 104 each.

The seven [percent] solution

Holmes was too busy with Moriarty to solve this case, but the Commonwealth did. The Queen will be very pleased that Canada came through on her behalf. On the following layout, winning the first trick and playing each suit including its ace through Trick 4 are absolutely essential to succeed — 7 out of 7 necessity — and the North-South hands each total 104.

3 NT S K 8 7 3 2
H A 7
D 10 8 7
C A 7 4
Leader
1. W
2. N
3. S
4. S
5. N
Lead
H K
S 8
D A
C Q
D 8
2nd
A
9
4
K
3rd
6
A
7
A
4th
2
5
3
2
S 5
H K Q J 10 5 4
D J 6 5 4
C K 5
Table S Q J 10 9 6
H 6
D K 9 3
C 9 8 6 2
S A 4
H 9 8 3 2
D A Q 2
C Q J 10 3

Dan Gheorghiu: There are eight top tricks, and spades, diamonds or clubs could provide a ninth. Trick 3 is critical for the defense: If East follows with a low diamond, a diamond is led at Trick 5 toward the queen, then East is eventually endplayed with the fourth club to take two spade tricks (ducked) then North scores the S 7. If East instead unblocks the D K (preserving an entry to partner’s jack), declarer cashes his clubs and S K, then exits with a heart to endplay West [assuming he keeps D J-x] to win the last two tricks in diamonds. If the court would call on me, I will do my civic duty to testify against South.

The evidence looks damning, so that rogue South declarer should pay for his evildoings. Pack your bags! Lestrade has booked you first class, but don’t head for the airport… it’s rail to New York, then the RMS Mauretania to London. Bon voyage!

This puzzle was inspired by an old double-dummy problem, Ace Grabber.

There are always some lunatics about

Charles Blair: “…wherever else that red herring [C 7] led your pack.” –The Adventure of the Priory School

Shouldn’t that be a black herring? Charles alludes to East’s curious C 9-8-6-2, suggesting a solution of C Q-J-10-7 opp. A-4-3, allowing four club winners (shades of Fail Safe). I wish I could claim such deviousness, but the noncritical E-W cards were chosen for an entirely different reason; in case nobody noticed, both E-W hands also total 104. Or as Holmes might put it: Lunacy breeds symmetry not subterfuge.

Inspector Lestrade: You know, Holmes? In another life you’d have made an excellent criminal.

Sherlock Holmes: Yes. And you, sir, an excellent policeman.

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Acknowledgments to Sir Arthur Conan Doyle (1859-1930)
© 2015 Richard Pavlicek