# A Bridge Puzzle

#### Andre

Can I amuse anybody with a bridge puzzle? I made it some 25 years ago and it took almost a year to debug it. So if you find the solution within minutes then that’s either brilliant or you found one of the two build-in traps. The real solution looks unusual.

South plays six No Trump, west leads the 6 of hearts. How is the contract made against any defence?

...........................Sp - J 9 6 5
...........................Ha – A Q 8 5
...........................Dia – A 5 3
...........................Cl – 9 3

Sp – 8 4 .....................................Sp - K 10 7 3 2
Ha - J 10 7 6 3 2...........................Ha – 9 4
Dia – K 10 9 7 6...........................Dia –
Cl - ............................................Cl – J 8 7 6 4 2

...........................Sp – A Q
...........................Ha – K
...........................Dia – Q J 8 4 2
...........................Cl – A K Q 10 5

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#### neurocomp2003

hmm interesting...guess the bidding doesn't matter and i'm assuming we play off the Defense hands(looking at it we attack E)...Do i assume standard convention that W will lead off the at least 5-length? Because some people don't play that way. The reason i ask is it appropriate to assume a 5-3 or 6-2 split in H

and it looks like you'll be going for 2S 3H 2D 4C and an extra S or C ...

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#### Andre

Don't worry about conventions. Peeking allowed, Open cards, no guesses.

#### neurocomp2003

I don't think its possible...I went through many scenarios of how the D would play.
(1) S wins with KH -> discovers 6-2, 5-3 split
(2) S wins with AC -> discovers 0-6 split
(3) and suit I play leads to only 11 tricks. I decided to go with the JD
either JD wins or KD to AD wins
-> discovers 5-0 split

Thus at this point S has discovered E10-E8...
he doesn't know how the spades are split and the last heart
1SH:6S 2S1H:5S OR 3S:4S1H

he's gotta win with a extra spade trick but i don't see how he can force E to play and if he allows W to win one trick he loses.

perhaps this is one of the traps you were discovering that i have fallen into

plz pm the answer...cuz i don't think it can be done

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#### Hurkyl

Staff Emeritus
Gold Member
You've barely looked at it, how can you be sure it can't be done? :tongue2:

East can be badly squeezed on the play of the red suits -- the problem would be easy because of that, if it weren't for the transportation problems. With the way the spots are, there are plenty of reasons to think an endplay might be feasible.

Not to mention some other interesting features that I'll keep quiet in case they're key, so I don't spoil it for anyone!

#### neurocomp2003

i barely worked on it? i worked on it for 3 hours

If you give W the lead you'll never win. you can't squeeze a trick outta the red suits and if W takes a trick of red you can't find an extra black suit winner.

The loser has to be a black suit...but if you force clubs E can can take 2 1C1S
So in the scenarios that i saw i had to win with the 9S but I can't force E to play anything.

I can see a win if S had one more spade or N had one more club...this is gonna mess me up for the rest of the night.

#### Andre

This is why it's called a brainteaser . It can be done, however you won't believe your eyes if you see how.

Consider that a hint. Perhaps try the most improbable. Furthermore a good bridge puzzle does not rely on finesses. Think squeezes, a lot of squeezes, well above the average.

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#### neurocomp2003

yeah but its aquestion of can the D over come any squeeze and i think they can. ...plz send me the solution =] perhaps the solution is wrong in terms of the D.

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#### Hurkyl

Staff Emeritus
Gold Member
Sorry, my mistake!

I'm not so sure on the red suits. You threaten to make a low heart or diamond trick (or two!), with a possible squeeze on west on the run of clubs. Not to mention that west might be used as an entry to north!

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#### neurocomp2003

heh how far have you gotta hurkyl..i've played like 100 hands of this on like 10 pieces of paper...each outcome making the D take 2. Because of:

we should all sit down and play this out =]

#### Hurkyl

Staff Emeritus
Gold Member
All right, I think this is the 5-th time I thought I had it! But I didn't see any mistakes this time! Woohoo!

Start off by cashing the K of hearts, and the AQ of spades.

Case 1: east takes the K of spades.
If east returns a spade or a low club, the rest is easy.
Suppose east returns a heart. Then, I'm in dummy with:

North: S: J 9 / H: Q 8 / D: A 5 3 / C: 9 3
West: S: - / H: J T 7 3 / D: K T 9 7 6 / C: -
South: S: - / H: - / D: Q J 8 4 / C: A K Q T 5

Now, I cash the jack of spades and three club tricks. West cannot pitch three hearts, but he can safely pitch two hearts (and thus only two diamonds), leaving:

North: S: - / H: Q 8 / D: A 5 3 / C: -
West: S: - / H: J T / D: K T 9 / C: -
South: S: - / H: - / D: Q J 8 4 / C: A

Whatever west pitches on the ace of clubs, I can take the rest.

Now, suppose instead east returned the jack of clubs way back when, leaving me in my hand, after west pitches a heart:

North: S: J 9 / H: A Q 8 / D: A 5 3 / C: 9
West: S: - / H: J T 7 3 / D: K T 9 7 6 / C: -
East: S: T 7 3 / H: 9 / D: - / C: 8 7 6 4 2
South: S: - / H: - / D: Q J 8 4 2 / C: A K T 5

So, I lead the Q of diamonds. Suppose west ducks, then I lead the jack of diamonds. West must cover, or else I take the rest. I then cash the top two hearts. In my hands, this leaves 5 cards :

North: S: J 9 / H: 8 / D: 5 / C: 9
East: ?
South: S: - / H: - / D: 8 / C: A K T 5

East must keep two spades and four clubs to stop both black suits, but has only 5 cards. Thus, I get the rest.

So, west must have covered the queen of diamonds, (east can safely pitch a spade) leaving me in dummy with:

North: S: J 9 / H: A Q 8 / D: 5 3 / C: 9
West: S: - / H: J T 7 3 / D: T 9 7 6 / C: -
East: S: T 7 / H: 9 / D: - / C: 8 7 6 4 2
South: S: - / H: - / D: J 8 4 2 / C: A K T 5

But now, I can take the rest in this order:
J of spades, AQ of hearts, 9 of clubs, J of diamonds, AKT of clubs

---------------------------------------------------------------

Case 2: East lets the Q of spades win, leaving this position with me in my hand:

North: S: J 9 / H: A Q 8 / D: A 5 3 / C: 9 3
West: S: - / H: J T 7 3 2 / D: K T 9 7 6 / C: -
East: S: K T 7 / H: 9 / D: - / C: J 8 7 6 4 2
South: S: - / H: - / D: Q J 8 4 2 / C: A K Q T 5

Now, I play out three diamonds and two hearts (losing a diamond). How do I do this?
I lead the Q of diamonds.
If west plays the K, I let it win. If a diamond is returned, I win with the jack, then cross to the ace, then take two hearts. If a heart is returned, I win, cash the J then A of diamonds, then cash the Q of hearts.
If west ducks the Q of diamonds, I then lose a diamond trick, win the return in dummy, and finish cashing the red suit tricks.

Either way, I'm in dummy with this:

North: S: J 9 / H: 8 / D: - / C: 9 3
South: S: - / H: - / D: - / C: A K Q T 5

East must keep one spade and 5 clubs to keep me from taking the rest of the tricks, but he only has 5 cards. Therefore, I take the rest of the tricks.

Phew, that was a mess!

#### neurocomp2003

very elegant solution, however:
you did something that i wouldn't have
dared at trick 4-6. You club finessed(without knowing distribution)
after losing a trick but it DID lead to the solution. But then again
this is opened brain teaser and thats why i'm not a pro player.

[1] when you claim KS to H to JS and then 3 club tricks.
You are finessing the JC right? otherwise the solution would fail.

[2] if E leads a low club instead of H what would you play?

again very nice solution

#### Andre

Good job Hurkyl.

Did you see what was wrong with leading the ten of clubs at trick two? (that took a while to debug as second solution)

#### Hurkyl

Staff Emeritus
Gold Member
It's a double dummy problem -- they usually have strange distributions and odd layouts, and you're expected to use knowledge of how the cards lie.

I'm pretty sure I would never come up with this line of play if I couldn't see the other hands!

If east returned a small club at trick 4, then he finesses himself in clubs, and gives me the 9 of clubs as an entry. I take the 9 in dummy and cash the jack of clubs and the hearts, then I come back to my hand (with the club finesse) to get the other 4 clubs, then two diamonds, for 2 + 3 + 2 + 5 tricks.

As for leading the T of clubs at the second trick, I hadn't worked very far along that line -- the spade blockage was a common theme in failed attempts at solutions, which is why I was focusing on the spades at trick 2. I think I have access to a double dummy solver, so I was going to run this problem through it to see what it thought.

#### neurocomp2003

for some reason i always thought bridges puzzles were so that you play it out as you would but you discover opps hands ass you play then thats why the opps hands were open handed...thats why i was going through discovering distribution. Didn't know you can play directly from knowing the opps hands...thats why the early club finesse was not appealing HEH I learned something new about bridges puzzles.

#### Hurkyl

Staff Emeritus
Gold Member
Well, there are (at least) two types of bridge puzzles. The normal ones, and the double dummy ones.

"A Bridge Puzzle"

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