Main     Puzzle 8N37 by Richard Pavlicek    

Just Another Zero

“Timothy, come here! I have a hand to show you from last night, playing with Marlon. I was East and picked up my usual garbage — though not bad for poker, with four nines against Marlon’s four sevens — only to watch our opponents bid and make six notrump. [The Professor jots down two hands on the back of a pickup slip.] Despite being a complete zero, it fuels my latest theory.”

6 NT South  ?
 ?
 ?
 ?
S J 10 7 6
H 7 6
D J 7 6 5
C Q 8 7
Table S 9 8 5 4
H Q J 9 8
D 9 8
C 10 9 6
West leads  ?
 ?
 ?
 ?

“A complete zero?” Timothy queried. “Must’ve been a weak field. You have two queens and three jacks between you, so North-South have 33 HCP. They also have no eight-card fit, so bidding and making 6 NT should be a normal result, albeit below average for you.”

“Yes, but Marlon could have beaten it. The remarkable fact is that we could not have beaten a slam in any of their seven-card fits. This follows directly from the corollary to my boson deflection theory: The rank sum of defensive quads, nines plus sevens, is zero (hexadecimal modulus) which, per the Law of Total Bosons, should equal the sum of suit slam undertricks. This is also zero, so we have a perfect correlation. But I’m sure you’re aware of that.”

“Yes, I’m well aware…” acknowledged Timothy, suppressing his true sentiment that the Professor was a nut case. For amusement he decided to play along, “But what if they bid the slam in spades? Surely there’s an undertrick there.”

“Get serious. Even Grover could beat that. And don’t make light of my theories! The Law only applies to majority trump fits, but I’m working on a general theory to encompass all. In college, I learned never to underestimate the power of trump.”

“I see. Apparently your alma mater was the Electoral College.”

Any more nut cases out there? Here’s your chance to practice zero tolerance:

Construct North-South hands to fit the story.

Many solutions exist. As a further goal (tiebreakers for the February 2017 contest) try to give North the best possible poker hand, and South the worst possible poker hand.

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Duncan Bell Wins!

In February 2017 this puzzle was presented as a challenge — with no help provided — inviting anyone who wished to submit a solution. Participation waned from last month’s peak (predictable perhaps with real defenders replacing my January morons) but 61 persons gave it at least one try. Only the 14 listed produced a layout to fit the story, which required 6 C, 6 D and 6 H to be the only makable six-bids by South.

Congratulations to Duncan Bell, England, who was the first of only three to find the optimal solution (best poker hand North and worst poker hand South). Duncan also won The Twelve of Spades in December, and despite being a late joiner to this series, might be “for whom the bell tolls” in the future. Placing second was another ringer, Leif-Erik Stabell, Zimbabwe; but the peals draw silent for Grant Peacock, Maryland, in third place. No, wait… [in my best Don Adams imitation] Would you believe a bell-shaped bird?

RankNameLocationNorthSouth
1Duncan BellEnglandSF-5432AFL-J5432
2Leif-Erik StabellZimbabweSF-5432AFL-J5432
3Grant PeacockMarylandSF-5432AFL-J5432
4Dean PokornyCroatiaSF-5432AFL-QT432
5Lin MurongOntarioSF-5432AFL-KT432
6Foster TomBritish ColumbiaSF-5432AFL-KT543
7Ray LiuOntarioSF-5432AFL-AKT43
8Tina DenleeQuebecSF-5432AFL-AKQ32
9Tim BroekenNetherlandsSF-5432AFH-KKKAA
10Nicholas GreerEnglandSF-5432AFH-AAAKK
11Charles BlairIllinoisSF-5432AFH-AAAKK
12Dan GheorghiuBritish Columbia4K-AAAAK2P-KKTTQ
13Brendan McDonaldAustralia4K-AAAAKFL-KT432
14Mike WenbleEngland4K-AAAAKFL-KT543

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Solution

This puzzle has many solutions, a whopping 137,351 by my analysis, so the crux was to find the best and worst poker hands for North and South, respectively. A few solvers overlooked the possibility of a lowball straight flush (5432A in hearts or clubs) no doubt because the ace is always high in bridge, thus settling on four aces as North’s best poker hand.

I liked this first deal from Dan Gheorghiu, British Columbia, because it was only entry that reduced South’s poker hand to a measly two pair (KKTTQ). Unfortunately, this was only the secondary tiebreaker, so North’s four aces placed him well down the list.

Dan Gheorghiu: In 6 NT declarer has 10 top tricks and can establish a heart by leading twice from dummy (giving up a trick) with potential for a positional squeeze against West’s minors; but this fails because hand entries are only in hearts, so dummy’s H A cannot be won before the top spades. Obviously, either major lead will defeat 6 NT, so perhaps Marlon led a minor to let it make.

Six of any suit (except spades) makes against any defense. Most interesting I thought was 6 H with a trump lead:

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

After six tricks South is on lead in the ending at right. If you cash the S Q you fail! Instead you must ruff a spade (the queen if you want to show off) and lead a good diamond.

East has no answer: (1) If he ruffs low, overruff and return to dummy in clubs; H A, etc. (2) If he ruffs high, you can draw his remaining trumps thanks to the two club entries. (3) If he pitches a club, cash C A-K before leading the last diamond.
South
leads
S
H A 4 3
D Q 4
C A K
S J 10
H 7
D J
C Q 8 7
Table S 9
H Q 9 8
D
C 10 9 6
S Q 3
H 10
D
C J 5 4 2

Grand eloquence

The story conditions — 6 C, 6 D and 6 H the only makable six-bids — were met by 14 successful solvers, but only one produced an overtrick. While immaterial in the ranking, Charles Blair, Illinois, earns style points for this entry cold for 7 D.

Constructions are possible to make both 7 D and 7 C (obviously not 7 H), e.g., North S A-K-Q-2 H A D A-K-Q-10 C A-K-J-2. None of these, however, would score high on the leaderboard, because North cannot be given a straight flush.

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

After a heart lead, South wins a top card in each suit (proving the lead doesn’t matter) then two top spades, a spade ruff, and two more winners to reach the ending at right.

A club is ruffed low, and declarer crossruffs the remainder, as West can only underruff and be trump-couped.
South
leads
S
H 5
D K 10 4
C
S
H
D J 7 6
C Q
Table S
H Q 9
D 9
C 10
S 3
H
D Q
C J 5

Charles Blair: I wonder if we could have six of any suit making but 6 NT going down.

Yes, in fact seven of any suit can be made with 6 NT failing. Examples are shown in Can You Solve a Mystery? (The ‘mystery’ was to create such a deal where even five notrump fails, but it remains unsolved and is now believed to be impossible, though unproved.)

Dual unblocking duel

The next entry from Dean Pokorny, Croatia, was the second-best effort, reducing South’s poker hand to a queen-high flush. The required suit slams (6 HDC) are relatively easy to make. Six notrump is defeated with a heart lead but requires careful defense by East.

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

Note the dual unblocking plays in clubs to leave the position at right. When declarer gives up a club, West can win and lead a second heart to foil communication. (If East won the third club, he could not lead a heart without losing a trick.)

Also note that declarer would have a double squeeze (treating the S Q like a deuce) if the D Q were cashed early, but doing so would allow West to cash the setting trick.
North
leads
S A 3 2
H K 3
D
C 5 4 3
S J 10 7 6
H 6
D J 7
C 8
Table S 9 8 5 4
H Q 9 8
D
C 6
S K Q
H 10 5 4
D Q 10 4
C

Foster Tom: Giving North a straight flush in clubs allows two clubs to be established, which necessitates a blocked position for 6 NT to fail.

Jack be nimble

The ultimate solution, found by three solvers, reduces South to a jack-high flush. Below is the winning entry from:

Duncan Bell: Leading hearts twice beats 6 NT by disrupting communications, which otherwise makes by establishing clubs. Six hearts makes by ruffing a spade and club in North, finessing a heart (East splitting) and leading a diamond at trick 11. Six diamonds makes, as clubs can be established without losing a trick; and 6 C plays similarly to 6 NT, except with trumps there are no communication problems.

The play in 6 H is perhaps the most interesting. Suppose West leads a diamond.

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

After winning the first 10 tricks with East following suit, the 3-card ending at right is reached. North leads the D Q, and East can win only one trick.

Not quite right, Richard.
The ending is four cards
(bosons invisible).
North
leads
S
H A 5
D Q
C
S
H 7
D J 7
C
Table S
H Q 9 8
D
C
S
H 10
D
C J 5

Most solvers who found the straight flush for North tried to reduce South’s poker hand further, but soon realized that a flush was inevitable. Any attempt to remove South’s 5-card suit results in 6 NT making or a suit slam failing.

Grant Peacock: If you give North a straight flush, South has a doubleton. I can’t make a 4-4-3-2 hand for South that works, so his poker hand has to be at least a flush, and J-5-4-3-2 is minimal.

Duncan Bell: I couldn’t give South less than a flush, since he can’t have more than two hearts (North needs a straight flush) or more than two diamonds (to threaten a ruff at trick 11).

Bosons in the news

Dan Gheorghiu: We all are aware of the Professor’s Law of Total Bosons. In the present case, however, Trump bosons might deflect from a wall and escape sideways, unless the wall is built completely around, in which case we Canadians may be coerced to pay for it. Hopefully, this would not block Internet access, so we’d still have the challenges and headaches of RP puzzles.

Tina Denlee: A complete zero, really? Applying your boson theory, I opened the East hand 2 D (both majors) which West converted to 2 S. North doubled for takeout, but South passed with S A-K-Q-3-2. Partner took one trick. Now that’s a complete zero — vulnerable, minus a two and three naughts (2000).

A painful lesson for Tina, Turner of the dummy, to watch Johnny Cash his tricks and Donald Trump the next.

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© 2017 Richard Pavlicek