Puzzle 8Q87   Main

# Cat o’ Nine Tales

by Richard Pavlicek

Once upon a time there was a kitten — not just an ordinary kitten, but an angelic messenger to bring happy memories of the good times. “Mabel Jr.” is no longer a kitten, now a year-and-a-half old, and she’s been bugging me to teach her bridge. No problem! I grabbed a deck of cards, dealt out two hands and asked her to bid something. She bid: “Meow, meow, meow!” Sorry, no threes. Go Fish! “M-mm-mm!” she purred with anxiety — so I fixed salmon for lunch, and now she thinks she’s a bridge player. Close enough.

Well, that’s one cat tale; I won’t bore you with eight more. Time for a puzzle! Each of the nine deals (A-I) has a common feature with one of the next nine deals (1-9). Your task is to pair them up. Simply select a letter for each number.

Matchmaker, matchmaker, make me a match! Or better yet, make nine!

 A Q 2 A Q 3 2 J 8 3 2 A 7 6 J 6 4 K 10 7 4 7 4 K Q 9 4 K 10 9 8 9 8 6 A 10 10 8 5 3 A 7 5 3 J 5 K Q 9 6 5 J 2 B 9 8 7 Q J 5 4 9 7 K Q 4 3 K Q 4 3 K 8 3 K Q 10 6 4 3 — J 5 A 9 7 2 A 2 10 9 8 7 6 A 10 6 2 10 6 J 8 5 A J 5 2 C 10 6 2 A K 6 5 A K Q A 9 8 9 8 7 3 Q 9 8 J 9 7 J 10 6 Q J 5 4 10 7 3 10 6 5 2 Q 5 A K J 4 2 8 4 3 K 7 4 3 2

 D A J 8 5 10 6 10 9 3 K J 5 4 K Q 10 2 8 7 5 5 4 A Q 10 9 9 A J 4 2 K Q 7 6 8 6 3 2 7 6 4 3 K Q 9 3 A J 8 2 7 E 5 6 4 3 A 8 5 2 A K 9 7 6 Q 8 2 K 10 7 K J 6 4 J 4 3 A J 10 9 7 3 A 5 2 9 7 Q 10 K 6 4 Q J 9 8 Q 10 3 8 5 2 F J 5 3 2 A 4 3 8 7 4 5 4 2 Q 10 8 7 10 A Q J 9 2 A K 8 9 6 4 Q J 9 2 K 6 5 9 7 3 A K K 8 7 6 5 10 3 Q J 10 6

 G Q 8 5 K Q 10 9 A 3 2 J 3 2 A K 2 J 5 10 8 Q 10 9 7 6 5 J 10 4 A 7 6 4 3 2 K 6 5 4 — 9 7 6 3 8 Q J 9 7 A K 8 4 H Q 5 3 A 10 8 J 7 6 3 Q 9 8 K 2 Q 3 A Q 10 9 5 K 7 6 2 10 9 4 K 7 6 K 8 4 2 A 10 4 A J 8 7 6 J 9 5 4 2 — J 5 3 I A J 9 6 3 K Q 10 8 5 4 8 4 5 4 J 9 7 2 Q A K Q 10 3 2 8 7 A 8 6 A K 9 7 6 3 2 5 K Q 10 2 5 4 3 J 10 J 9 7 6

 1  ?ABCDEFGHI A 5 4 3 J 8 2 K 9 6 3 J 2 J 7 K 5 4 3 Q 7 2 K 10 6 3 K 10 9 6 Q 7 A 10 5 4 Q 8 7 Q 8 2 A 10 9 6 J 8 A 9 5 4 2  ?ABCDEFGHI 4 K Q 8 6 3 K Q J 9 7 9 3 A 7 5 — A 8 6 5 3 2 A J 7 6 Q J 9 6 3 2 A 10 10 10 5 4 2 K 10 8 J 9 7 5 4 2 4 K Q 8 3  ?ABCDEFGHI K 7 6 4 6 4 K 8 5 4 A 8 7 10 5 2 8 3 A J 6 3 K Q 9 6 A J K J 9 5 Q 10 9 J 5 4 3 Q 9 8 3 A Q 10 7 2 7 2 10 2

 4  ?ABCDEFGHI K Q 7 5 2 J 9 7 6 3 8 5 4 A 10 2 J 9 7 6 8 5 A J 10 2 8 5 4 3 A 8 4 A K Q 10 K Q J 9 6 K Q 10 3 4 2 9 7 6 3 5  ?ABCDEFGHI A 4 3 A Q J 3 2 A 9 8 7 5 Q 8 7 2 9 6 K 7 6 5 J 6 4 J 9 6 5 4 3 A K J 5 2 10 8 — K 10 Q 10 8 7 9 4 K Q 10 3 2 6  ?ABCDEFGHI 9 3 Q J 10 7 A Q 4 J 7 4 2 J 9 8 6 2 J 7 2 A K Q 10 3 K 7 6 4 A K K 6 5 3 9 8 6 A Q 10 8 5 2 5 4 3 10 9 8 5

 7  ?ABCDEFGHI J 10 6 5 A K 8 3 2 K 3 10 6 A 2 Q 4 A 9 7 2 A J 8 5 2 — J 5 J 10 8 6 5 K Q 9 7 4 3 K Q 9 8 7 4 3 10 9 7 6 Q 4 — 8  ?ABCDEFGHI J 9 K J 10 9 K J 10 Q 10 8 2 — A Q 4 2 A 8 7 6 5 2 J 6 4 10 8 5 3 2 7 6 3 9 4 3 7 5 A K Q 7 6 4 8 5 Q A K 9 3 9  ?ABCDEFGHI 6 3 2 K Q 9 3 7 6 A J 8 2 A J 8 5 10 6 K J 5 4 10 9 6 K Q 10 8 7 5 A Q 10 9 5 4 3 9 7 4 A J 4 2 8 3 2 K Q 7

Correct pairing is based on the most unlikely common feature, so trivial matches like “both deals have a club void” rate to be as successful as Mabel Jr. playing 7 NT doubled. Deals are also available in RBN and PBN format.

## Duncan Bell Wins

This puzzle contest ran from November 5-30, 2021. I am embarrassed to say there were only six participants, and to get even that many I had to extend beyond the human race. I thought interest would be higher, especially with many people homebound by the pandemic, if not for the mental challenge at least for the lottery aspect; or maybe the 362,879 to 1 odds against guessing them all right was too prohibitive. Oh well. I haven’t hit zero yet! Maybe next time.

Three of the five human solvers were correct on all matches, but only Duncan Bell provided all the right reasons. This is hardly a surprise and fittingly is Duncan’s cat o’ninth win in my puzzle contests. His previous eight wins were The Twelve of Spades, Just Another Zero, High Stakes Rubber, Frozen, Bridge with the Abbott, Pay No Taxes!, High Cards Amiss and Middle School Mania. Further, he accomplished this in less than five years, which percentagewise puts him ahead of my all-time leader, Tim Broeken (Netherlands).

Florida makes a comeback! After a long absence from my leaderboards, the return of my home state brings great felinity, I mean felicity. Mabel Jr. actually chose the matches, as I put her treats in a tic-tac-toe grid, and the order she ate them became her choices. Okay, okay, I’m a cheetah, as I coaxed her into some right choices, lest she end up in a catatonic state — is that Florida?

Winner List
RankNameLocationCorrectReasons
1Duncan BellEngland99
2Richard SteinWashington98
3Nicholas GreerEngland96
4Mabel Pavlicek Jr.Florida6Meow × 6

 Puzzle 8Q87   Main Top   Cat o’ Nine Tales

## Solutions

Five of the nine matches are related to makable contracts, so to aid recognition, each deal is accompanied by a 4×5 matrix of winnable tricks for each player in each strain, assuming purrfect play all-around.

1

A 5 4 3
J 8 2
K 9 6 3
J 2
J 7
K 5 4 3
Q 7 2
K 10 6 3
K 10 9 6
Q 7
A 10 5 4
Q 8 7
Q 8 2
A 10 9 6
J 8
A 9 5 4
 1NSWE N7777 6688 8866 6688 8866

 HNSWE N7777 8855 8855 7766 8855
H

Q 5 3
A 10 8
J 7 6 3
Q 9 8
K 2
Q 3
A Q 10 9 5
K 7 6 2
10 9 4
K 7 6
K 8 4 2
A 10 4
A J 8 7 6
J 9 5 4 2

J 5 3

Everybody makes 1 NT! Nothing but sevens under the N (notrump) shows that whoever declares 1 NT can make it against any defense. The implication of this phenomenon is that all hands are endplayed on the opening lead; whichever suit is led costs a trick.

Duncan Bell: One notrump makes by all hands. This and all contract related claims that follow are with best play at double-dummy.

Richard Stein: Opening lead zugzwang; 1 NT makes by anyone.

2

4
K Q 8 6 3
K Q J 9 7
9 3
A 7 5

A 8 6 5 3 2
A J 7 6
Q J 9 6 3 2
A 10
10
10 5 4 2
K 10 8
J 9 7 5 4 2
4
K Q 8
 2NSWE N7766 101033 8855 8855 9944

 ENSWE N5588 3399 331010 4488 2299
E

5
6 4 3
A 8 5 2
A K 9 7 6
Q 8 2
K 10 7
K J 6 4
J 4 3
A J 10 9 7 3
A 5 2
9 7
Q 10
K 6 4
Q J 9 8
Q 10 3
8 5 2

Only makable game is a 3-3 fit! Believe it or not, N-S make 4 on Deal 2, and E-W make 4 on Deal E. All other game contracts fail.

Nicholas Greer: Each deal has only one makeable game, and it’s in a 3-3 fit.

Makable or makeable? I thought these were just alternate spellings, but an online search showed a difference. “Makable” means capable to be made, while “makeable” means able to be made, and only the latter allows comparative forms (more makeable, most makeable). Therefore, “makable” is correct for double-dummy bridge purposes.

3

K 7 6 4
6 4
K 8 5 4
A 8 7
10 5 2
8 3
A J 6 3
K Q 9 6
A J
K J 9 5
Q 10 9
J 5 4 3
Q 9 8 3
A Q 10 7 2
7 2
10 2
 3NSWE N7756 8855 7755 6677 7766

 GNSWE N5555 7644 331010 5577 9933
G

Q 8 5
K Q 10 9
A 3 2
J 3 2
A K 2
J 5
10 8
Q 10 9 7 6 5
J 10 4
A 7 6 4 3 2
K 6 5 4

9 7 6 3
8
Q J 9 7
A K 8 4

All four hands have the same Kaplan-Rubens point count: 10.60 on Deal 3, and 11.20 on Deal G. This phenomenon is extremely rare because of the fine gradation (0.05 increments). K-R points can be found for any hand with my Bridge Hand Evaluator. For a complete explanation see Kaplan-Rubens Evaluation Stats.

Duncan Bell: All hands have equal K-R point counts to at least one decimal place.

4

K Q 7
5 2
J 9 7 6 3
8 5 4
A 10 2
J 9 7 6
8 5
A J 10 2
8 5 4 3
A 8 4
A K Q 10
K Q
J 9 6
K Q 10 3
4 2
9 7 6 3
 4NSWE N5577 4488 7755 4499 7755

 INSWE N2277 4499 5577 221111 8855
I

A J 9 6 3
K Q 10
8 5 4
8 4
5 4
J 9 7 2
Q
A K Q 10 3 2
8 7
A 8 6
A K 9 7 6 3 2
5
K Q 10 2
5 4 3
J 10
J 9 7 6

Card ranks in each suit are alphabetic. For instance, Ace-Jack-Nine-Six-Three. The longest possible alphabetic suit is seven cards; East’s diamonds on Deal I is one of only three such holdings. For more than you’d ever want to know on this topic see Alphabetic Suits.

Richard Stein: Those suits look suspicious, but I can’t quite herd every kitten… [Aha!] All suit holdings in standard order are also in alphabetical order.

Alphabetic or alphabetical? Although casually interchangeable, proper distinction found online is that “alphabetic” means relating to an alphabet, while “alphabetical” means arranged in the order of an alphabet. This makes my usage wrong — so sue me — and “alphabetical order” is redundant, as it should be “alphabetic order” or one word “alphabetical.”

5

A
4 3
A Q J 3 2
A 9 8 7 5
Q 8 7 2
9 6
K 7 6 5
J 6 4
J 9 6 5 4 3
A K J 5 2
10 8

K 10
Q 10 8 7
9 4
K Q 10 3 2
 5NSWE N5588 33109 33910 33109 6577

 CNSWE N3388 33109 33910 331010 6677
C

10 6 2
A K 6 5
A K Q
A 9 8
9 8 7 3
Q 9 8
J 9 7
J 10 6
Q J 5 4
10 7 3
10 6 5 2
Q 5
A K
J 4 2
8 4 3
K 7 4 3 2

The only makable games are 4 by West and 4 by East. The need to right-side contracts is common, but what’s right for one is almost always right for another. Opposite right-siding is rare. For the record, 4  by East is defeated by a diamond lead on Deal 5 and a heart lead on Deal C; 4  by West is defeated by a trump lead on Deal 5 and the J lead on Deal C.

Duncan Bell: Game in both majors, but one only makes declared by East and the other declared by West.

6

9 3
Q J 10 7
A Q 4
J 7 4 2
J
9 8 6 2
J 7 2
A K Q 10 3
K 7 6 4
A K
K 6 5 3
9 8 6
A Q 10 8 5 2
5 4 3
10 9 8
5
 6NSWE N5566 6655 5566 4466 6666

 ANSWE N6666 6666 6666 6656 6666
A

Q 2
A Q 3 2
J 8 3 2
A 7 6
J 6 4
K 10 7 4
7 4
K Q 9 4
K 10 9 8
9 8 6
A 10
10 8 5 3
A 7 5 3
J 5
K Q 9 6 5
J 2

No player makes any contract! Not a seven in sight shows that any bid results in a minus score against best defense — a perfect passout, or “par zero” deal. My database of 10,485,760 random solved deals has only 25 of these, so it’s about a 0.0002 percent chance.

Nicholas Greer: No makeable contract for anyone.

Let this be a warning: One more “makeable” and you’re outta here!

7

J 10 6 5
A K 8 3 2
K 3
10 6
A 2
Q 4
A 9 7 2
A J 8 5 2

J 5
J 10 8 6 5
K Q 9 7 4 3
K Q 9 8 7 4 3
10 9 7 6
Q 4
 7NSWE N7766 101033 6755 5588 4499

 BNSWE N5533 111022 6476 101033 4588
B

9 8 7
Q J 5 4
9 7
K Q 4 3
K Q 4 3
K 8 3
K Q 10 6 4 3

J 5
A 9 7 2
A 2
10 9 8 7 6
A 10 6 2
10 6
J 8 5
A J 5 2

Card ranks in each suit are symmetric. An eight is the middle rank, so every odd-length suit must contain it. Otherwise, each ace must pair with a two, each king with a three, etc. And who could argue that a void is not symmetric? A corrolary to symmetric suits is that each hand must have the same total rank count: 13 × 8 = 104 (A=14 K=13 …). For more on this silliness see Symmetric Suits.

Richard Stein: All suit holdings are symmetrical about the median rank, eight.

Symmetric or symmetrical? Online consensus is the words have identical meanings and are interchangeable, though I found two plausible distinctions: (1) “Symmetric” is more often used in technical fields. (2) “Symmetric” takes two arguments, but “symmetrical” takes only one: If the left and right halves of a face are symmetric, then the face is symmetrical.

8

J 9
K J 10 9
K J 10
Q 10 8 2

A Q 4 2
A 8 7 6 5 2
J 6 4
10 8 5 3 2
7 6 3
9 4 3
7 5
A K Q 7 6 4
8 5
Q
A K 9 3
 8NSWE N9922 101022 101033 111122 111122

 FNSWE N9933 101033 101033 111122 111111
F

J 5 3 2
A 4 3
8 7 4
5 4 2
Q 10 8 7
10
A Q J 9 2
A K 8
9 6 4
Q J 9 2
K 6 5
9 7 3
A K
K 8 7 6 5
10 3
Q J 10 6

N-S make game exactly in every strain! Three notrump, four of a major, five of a minor — you name it, N-S make it (but no overtricks). My database has only 15 such deals. Checking E-W adds another 19, which makes the chance for either side about 0.0003 percent.

Mabel Pavlicek Jr.: 3 NT meow, 4 meow, 4 meow, 5 meow, 5 meow.

9

6 3 2
K Q 9 3
7 6
A J 8 2
A J 8 5
10 6
K J 5 4
10 9 6
K Q 10
8 7 5
A Q 10 9
5 4 3
9 7 4
A J 4 2
8 3 2
K Q 7
 9NSWE N331010 4488 4499 4499 3399

 DNSWE N9944 9934 8844 7745 7766
D

A J 8 5
10 6
10 9 3
K J 5 4
K Q 10 2
8 7 5
5 4
A Q 10 9
9
A J 4 2
K Q 7 6
8 6 3 2
7 6 4 3
K Q 9 3
A J 8 2
7

Best poker hand is two pair. For a bridge hand this is the worst possible (one pair is impossible because the remaining unmatched cards must form a straight). The chance of this in all four hands is 0.0018 percent.

Nicholas Greer: On both deals one side makes 3 NT but no suit game with only 21 HCP.

True of course, but empirical analysis shows this to be 0.2322 percent for exactly 21 HCP (0.3922 for 21 or fewer) which is 129 (218) times more likely than the poker scenario.

Duncan Bell: Best poker hand on each deal is QQTTA.

Certainly acceptable, and even less likely than my given reason. However, no catnip for:

Richard Stein: Worst possible poker pot winner: QQTTA. Not sure of this…

I couldn’t accept this reason because it’s not true. I believe the following deal has the worst possible poker hands:

 9 8 7 A K 5 Q 10 7 4 10 5 3 J 3 2 9 8 7 A K 6 Q J 4 2 Q 10 5 4 10 6 3 9 8 5 A K 6 A K 6 Q J 4 2 J 3 2 9 8 7

North and South would split the pot with jacks and deuces, over West’s 10s and sevens, and East’s 10s and sixes, each with an ace kicker. For a clear win (no tie) it takes jacks and threes, e.g., swap the 4 and 3. For more on bridge and poker see World Series of Bridge.

## Final Catcalls

Richard Stein: I wanted to verify my answers, but my cat allergies are kicking in. Ah-choo!

Anony-mouse: Enough with the puzzles! I am trying to improve my bridge game, and you waste my time with some stupid cat-and-mouse game. Get a life, you grimalkin addict!

Mabel Pavlicek Jr.: Don’t believe anything you read here! I was correct on all nine matches and submitted my entry two days before this Duncan donut dude.

 Puzzle 8Q87   Main Top   Cat o’ Nine Tales