Brain Teasers and Logic Puzzles

Zardoz · **Posted:** Tue Jul 24, 2012 13:58

Doctor Glyndwr wrote:

How much gold can the pirate captain keep for himself?

Aaaaaaarf.

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

He gives some to Pirate 1 and Pirate 3 and keeps the rest for himself. 1, 1 and 98 coins.

Because Pirate 1 and Pirate 3 are fucked with any other in the four pirate scenario, and 1 gold is the best offer they're going to ever get. And he needs the votes of two other pirates and his own vote to secure at least 50% and avoid execution.

That along the right lines?

edit: It's a good one this! You have to work backwards from what would happen if only one pirate was remaining up to the five pirates to see who gets what and which vote would be in their best interests at each stage.

Malc · **Posted:** Tue Jul 24, 2012 14:03

Doctor Glyndwr wrote:

Grim... wrote:

Here's one while we wait:

Are we waiting on me? Is that how this works?

OK, here's one:

Quote:

Five pirates have 100 gold coins. They have to divide up the loot. In order of seniority (suppose pirate 5 is the captain, pirate 1 is least senior), the most senior pirate proposes a distribution of the loot. They vote and if at least 50% accept the proposal, the loot is divided as proposed. Otherwise the most senior pirate is executed, and they start over again with the next senior pirate. What solution does the most senior pirate propose? Assume they are very intelligent and extremely greedy (and that they would prefer not to die).

How much gold can the pirate captain keep for himself?

If they have to be in order, then if there are 4 pirates, they could suggest 49,48,2,1, then the 2 would vote yes for that, and keep that, so the only way the captain can get more is if he gives pirates 3 and 4 more money than that.

So if he went for 86,5,4,3,2 then pirates 3 and 4 (if they were clever) would vote for it.

Malc

Doctor Glyndwr · **Joined:** 30th Mar, 2008 **Posts:** 32624

Malc wrote:

So if he went for 86,5,4,3,2 then pirates 3 and 4 (if they were clever) would vote for it.

That's not the optimial solution, the captain can keep more.

WTB wrote:

edit: It's a good one this! You have to work backwards from what would happen if only one pirate was remaining up to the five pirates to see who gets what and which vote would be in their best interests at each stage.

Yeah, I like this puzzle a lot.

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Malc wrote:

Doctor Glyndwr wrote:

Grim... wrote:

Here's one while we wait:

Are we waiting on me? Is that how this works?

OK, here's one:

Quote:

Five pirates have 100 gold coins. They have to divide up the loot. In order of seniority (suppose pirate 5 is the captain, pirate 1 is least senior), the most senior pirate proposes a distribution of the loot. They vote and if at least 50% accept the proposal, the loot is divided as proposed. Otherwise the most senior pirate is executed, and they start over again with the next senior pirate. What solution does the most senior pirate propose? Assume they are very intelligent and extremely greedy (and that they would prefer not to die).

How much gold can the pirate captain keep for himself?

If they have to be in order, then if there are 4 pirates, they could suggest 49,48,2,1, then the 2 would vote yes for that, and keep that, so the only way the captain can get more is if he gives pirates 3 and 4 more money than that.

So if he went for 86,5,4,3,2 then pirates 3 and 4 (if they were clever) would vote for it.

Malc

I think you're neglecting the issue with seniority. That mixes everything up.

Cras · **Joined:** 30th Mar, 2008 **Posts:** 49252

The bottom two would never vote for anything, because the best case for them is that the top three get bumped off and then they split it 50-50. So the captain needs to secure the two down from him. So optimal to secure the votes would probably be 34:32:31:2:1

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Craster wrote:

The bottom two would never vote for anything, because the best case for them is that the top three get bumped off and then they split it 50-50. So the captain needs to secure the two down from him. So optimal to secure the votes would probably be 34:32:31:2:1

Wrong! If two were remaining, the fourth pirate would take 100 gold.

Cras · **Joined:** 30th Mar, 2008 **Posts:** 49252

Oh yeah - he would get 50% of the vote. Dunno then.

Malc · **Posted:** Tue Jul 24, 2012 14:12

No, I misread it, I thought that it meant pirate 1 had to get more than pirate 2, who both had to be more than pirate 3 and so on.

Malc

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Pirate 1 remaining only: 100G
2 and 1: 100G, 0G
3, 2 and 1: 99G, 0G, 1G - Pirate 1 would settle for 1G because it's the best he's ever going to get. The 1 pirate scenario couldn't possibly happen.
4, 3, 2 and 1: 99G, 0G, 1G, 0G - Pirate 4 can get Pirate 2 on his side with 1G because that's the best he's ever going to get - in the next scenario he gets nothing.

Therefore, Pirate 5 can distribute as follows: 98G, 0G, 1G, 0G, 1G - Pirate 5 (the Captain), can rely on Pirate 3 and Pirate 1 because they get nothing in the next scenario.

I've gotta be right!

Doctor Glyndwr · **Joined:** 30th Mar, 2008 **Posts:** 32624

WTB is right on the money.

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Wahoo! Again, I'm all out of puzzles... Someone else's turn! In the meantime, I'll find one for my next go...

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

No wait, I've got one!

markg · **Joined:** 30th Mar, 2008 **Posts:** 16706

markg wrote:

Here's one that took me ages to figure out. It annoyed me for so long that I remember hearing it about twenty years ago and still have the solution in my head.

You have twelve identical looking red snooker balls and a pair of balances. One of the balls is slightly different in weight to all the others and you can use the balances only three times. Using only the balls and the balances you need to identify the different ball and say whether it is heavier or lighter than the others.

Curiosity · **Posted:** Tue Jul 24, 2012 14:25

markg wrote:

Here's one that took me ages to figure out. It annoyed me for so long that I remember hearing it about twenty years ago and still have the solution in my head.

You have twelve identical looking red snooker balls and a pair of balances. One of the balls is slightly different in weight to all the others and you can use the balances only three times. Using only the balls and the balances you need to identify the different ball and say whether it is heavier or lighter than the others.

Weigh 1-4 against 5-8

If equal, weigh 9-10 against 1-2

If equal weigh 11 against 1 (if equal 12 is the weirdo. You're using balls 1-2 as known equal weights. If 9-10 and 1-2 were unequal then weigh 9).

If 1-4 differs from (say heavier, can always reverse it) 5-8 it gets trickier

Weigh 1,2,5 vs 3,6,9

If equal ball is in 4,7,8 with either 4 heavy or 7 light or 8 light. Weigh 7v8. If equal 4 is heavy. If not, whichever is lighter is the odd ball.

If 1,2,5 heavier than 3,6,9 then 1 or 2 is heavy, or 6 is light. Weigh 1v2. If equal, 6 is light, if unequal heavier is heavy ball.

Etc for the raining branches of the tree

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Two trains enter a 200 mile tunnel at opposite ends at precisely the same time on the same track, heading in opposite directions. The trains are both travelling at 100mph.

The very moment the trains enter the tunnel, a "supersonic bee" flies from the front of one train to the front of the other at 1000mph, the moment it reaches the other train, it turns round and heads back to the first train. The bee continues to make this journey until the moment the trains collide.

How far did the bee travel?

edit: Whoops, sorry markg!

Curiosity · **Posted:** Tue Jul 24, 2012 14:28

An easy one:

You're blindfolded and handed a deck of card with 'N' cards flipped within the deck.

You need to divide the deck into two piles, each of which contains an equal number of flipped cards.

How do you do it without cheating, removing blindfold, etc.

zaphod79 · **Joined:** 16th Apr, 2008 **Posts:** 14534

WTB wrote:

Two trains enter a 200 mile tunnel at opposite ends at precisely the same time on the same track, heading in opposite directions. The trains are both travelling at 100mph.

The very moment the trains enter the tunnel, a "supersonic bee" flies from the front of one train to the front of the other at 1000mph, the moment it reaches the other train, it turns round and heads back to the first train. The bee continues to make this journey until the moment the trains collide.

How far did the bee travel?

edit: Whoops, sorry markg!

1000 miles ? (if the trains both are going at 100mph then in one hour they would collide - so the bee will have gone its max amount in that time)

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Curiosity wrote:

An easy one:

You're blindfolded and handed a deck of card with 'N' cards flipped within the deck.

You need to divide the deck into two piles, each of which contains an equal number of flipped cards.

How do you do it without cheating, removing blindfold, etc.

Remove 'N' cards from the pack and flip them over.

Say there are 10 cards flipped in the pack, and let's say that removing 10 from anywhere in the deck would result in a pile with 3 flipped cards - that means there are 7 flipped cards in the main deck still. Therefore flipping the 10 over would then mean that pile has 7 flipped cards as well.

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

zaphod79 wrote:

WTB wrote:

Two trains enter a 200 mile tunnel at opposite ends at precisely the same time on the same track, heading in opposite directions. The trains are both travelling at 100mph.

The very moment the trains enter the tunnel, a "supersonic bee" flies from the front of one train to the front of the other at 1000mph, the moment it reaches the other train, it turns round and heads back to the first train. The bee continues to make this journey until the moment the trains collide.

How far did the bee travel?

edit: Whoops, sorry markg!

1000 miles ? (if the trains both are going at 100mph then in one hour they would collide - so the bee will have gone its max amount in that time)

Correct!

markg · **Joined:** 30th Mar, 2008 **Posts:** 16706

Curiosity wrote:

markg wrote:

Here's one that took me ages to figure out. It annoyed me for so long that I remember hearing it about twenty years ago and still have the solution in my head.

You have twelve identical looking red snooker balls and a pair of balances. One of the balls is slightly different in weight to all the others and you can use the balances only three times. Using only the balls and the balances you need to identify the different ball and say whether it is heavier or lighter than the others.

Weigh 1-4 against 5-8

If equal, weigh 9-10 against 1-2

If equal weigh 11 against 1 (if equal 12 is the weirdo. You're using balls 1-2 as known equal weights. If 9-10 and 1-2 were unequal then weigh 9).

If 1-4 differs from (say heavier, can always reverse it) 5-8 it gets trickier

Weigh 1,2,5 vs 3,6,9

If equal ball is in 4,7,8 with either 4 heavy or 7 light or 8 light. Weigh 7v8. If equal 4 is heavy. If not, whichever is lighter is the odd ball.

If 1,2,5 heavier than 3,6,9 then 1 or 2 is heavy, or 6 is light. Weigh 1v2. If equal, 6 is light, if unequal heavier is heavy ball.

Etc for the raining branches of the tree

Yeah, it was harder before Google.

Curiosity · **Posted:** Tue Jul 24, 2012 14:31

zaphod79 wrote:

WTB wrote:

Two trains enter a 200 mile tunnel at opposite ends at precisely the same time on the same track, heading in opposite directions. The trains are both travelling at 100mph.

The very moment the trains enter the tunnel, a "supersonic bee" flies from the front of one train to the front of the other at 1000mph, the moment it reaches the other train, it turns round and heads back to the first train. The bee continues to make this journey until the moment the trains collide.

How far did the bee travel?

edit: Whoops, sorry markg!

1000 miles ? (if the trains both are going at 100mph then in one hour they would collide - so the bee will have gone its max amount in that time)

Half that. They're travelling towards each other.

Curiosity · **Posted:** Tue Jul 24, 2012 14:33

markg wrote:

Curiosity wrote:

markg wrote:

Here's one that took me ages to figure out. It annoyed me for so long that I remember hearing it about twenty years ago and still have the solution in my head.

You have twelve identical looking red snooker balls and a pair of balances. One of the balls is slightly different in weight to all the others and you can use the balances only three times. Using only the balls and the balances you need to identify the different ball and say whether it is heavier or lighter than the others.

Weigh 1-4 against 5-8

If equal, weigh 9-10 against 1-2

If equal weigh 11 against 1 (if equal 12 is the weirdo. You're using balls 1-2 as known equal weights. If 9-10 and 1-2 were unequal then weigh 9).

If 1-4 differs from (say heavier, can always reverse it) 5-8 it gets trickier

Weigh 1,2,5 vs 3,6,9

If equal ball is in 4,7,8 with either 4 heavy or 7 light or 8 light. Weigh 7v8. If equal 4 is heavy. If not, whichever is lighter is the odd ball.

If 1,2,5 heavier than 3,6,9 then 1 or 2 is heavy, or 6 is light. Weigh 1v2. If equal, 6 is light, if unequal heavier is heavy ball.

Etc for the raining branches of the tree

Yeah, it was harder before Google.

Nah, I just remembered it from a while back.

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Curiosity wrote:

zaphod79 wrote:

WTB wrote:

Two trains enter a 200 mile tunnel at opposite ends at precisely the same time on the same track, heading in opposite directions. The trains are both travelling at 100mph.

The very moment the trains enter the tunnel, a "supersonic bee" flies from the front of one train to the front of the other at 1000mph, the moment it reaches the other train, it turns round and heads back to the first train. The bee continues to make this journey until the moment the trains collide.

How far did the bee travel?

edit: Whoops, sorry markg!

1000 miles ? (if the trains both are going at 100mph then in one hour they would collide - so the bee will have gone its max amount in that time)

Half that. They're travelling towards each other.

200 mile tunnel!

markg · **Joined:** 30th Mar, 2008 **Posts:** 16706

Curiosity wrote:

markg wrote:

Curiosity wrote:

markg wrote:

Here's one that took me ages to figure out. It annoyed me for so long that I remember hearing it about twenty years ago and still have the solution in my head.

You have twelve identical looking red snooker balls and a pair of balances. One of the balls is slightly different in weight to all the others and you can use the balances only three times. Using only the balls and the balances you need to identify the different ball and say whether it is heavier or lighter than the others.

Weigh 1-4 against 5-8

If equal, weigh 9-10 against 1-2

If equal weigh 11 against 1 (if equal 12 is the weirdo. You're using balls 1-2 as known equal weights. If 9-10 and 1-2 were unequal then weigh 9).

If 1-4 differs from (say heavier, can always reverse it) 5-8 it gets trickier

Weigh 1,2,5 vs 3,6,9

If equal ball is in 4,7,8 with either 4 heavy or 7 light or 8 light. Weigh 7v8. If equal 4 is heavy. If not, whichever is lighter is the odd ball.

If 1,2,5 heavier than 3,6,9 then 1 or 2 is heavy, or 6 is light. Weigh 1v2. If equal, 6 is light, if unequal heavier is heavy ball.

Etc for the raining branches of the tree

Yeah, it was harder before Google.

Nah, I just remembered it from a while back.

Curiosity · **Posted:** Tue Jul 24, 2012 14:34

WTB wrote:

Curiosity wrote:

zaphod79 wrote:

WTB wrote:

Two trains enter a 200 mile tunnel at opposite ends at precisely the same time on the same track, heading in opposite directions. The trains are both travelling at 100mph.

The very moment the trains enter the tunnel, a "supersonic bee" flies from the front of one train to the front of the other at 1000mph, the moment it reaches the other train, it turns round and heads back to the first train. The bee continues to make this journey until the moment the trains collide.

How far did the bee travel?

edit: Whoops, sorry markg!

1000 miles ? (if the trains both are going at 100mph then in one hour they would collide - so the bee will have gone its max amount in that time)

Half that. They're travelling towards each other.

200 mile tunnel!

Whatevs.

Did you account for relativistic time dilation?

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

We need ONE new puzzle guys, preferably from zaphod, because he got mine right. Unless he wants to pass his win on. Pretty sure I got Curio's card one right.

zaphod79 · **Joined:** 16th Apr, 2008 **Posts:** 14534

WTB wrote:

We need ONE new puzzle guys, preferably from zaphod, because he got mine right. Unless he wants to pass his win on. Pretty sure I got Curio's card one right.

I'll pass

Curiosity · **Posted:** Tue Jul 24, 2012 14:36

WTB wrote:

We need ONE new puzzle guys, preferably from zaphod, because he got mine right. Unless he wants to pass his win on. Pretty sure I got Curio's card one right.

Jah!

Mr Dom · **Posted:** Tue Jul 24, 2012 14:46

In a magical land, with unicorns & shit, they have magic poisons so if you are poisoned, you just need to drink a stronger poison and it will cancel the weaker one. If you drink a weaker one second, it wont work & you die.

The king wants the strongest poison in the land so he can use it as an antidote, so he challenges the 2 best poisoners to a contest. Each one must bring a flask, and then they both drink from their opponents flask before drinking from their own. If their poison is the best, they will live.

However, the second best poisoner figures he can't beat the best, so comes up with a cunning scheme.
But, the best poisoner knows he is the best, and realises the second would need a cunning plan instead. So he works out what the second best was planning, and works out a counter-strategy.

On the day of the contest, the best poisoner wins.
Shortly afterwards, the king gets poisoned, tries the antidote, and dies horribly.

So...
The question is, why did the king die?

Malc · **Posted:** Tue Jul 24, 2012 14:46

If we knew it was definitly heavier, (or lighter) then I think I could do it, but as we don't know, the best I can do is the following.

Number the balls 1-12, split them 1-6 / 7-12, note which is heavier.

Then split them even/odd, note which is heavier

Assuming the odd/high numbers was heavier, then you know the ball is either 7,9,11 or 2,4,6.

So weigh 2 and 4 against 7 and 9, and then I'm out

Malc

Cras · **Joined:** 30th Mar, 2008 **Posts:** 49252

Mr Dom wrote:

why did the king die?

He went up against a Sicilian when death was on the line?

GazChap · **Posted:** Tue Jul 24, 2012 14:48

Craster wrote:

If D sees that they are the same, he will call out because his must be the other colour. If he sees that they are different, he cannot call out because he won't know..

C can therefore tell that if D has not called out, C's hat must be different from B's hat - so he can then call out because he now knows his colour.

Admittedly, the puzzle does rather assume that D and C are intelligent.

Which is unlikely, because if they were they wouldn't have allowed themselves to get put into this situation in the first place.

zaphod79 · **Joined:** 16th Apr, 2008 **Posts:** 14534

Mr Dom wrote:

The question is, why did the king die?

The king is one of the two best poisoners ?

Mr Dom · **Posted:** Tue Jul 24, 2012 14:51

zaphod79 wrote:

Mr Dom wrote:

The question is, why did the king die?

The king is one of the two best poisoners ?

Nope

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Mr Dom wrote:

In a magical land, with unicorns & shit, they have magic poisons so if you are poisoned, you just need to drink a stronger poison and it will cancel the weaker one. If you drink a weaker one second, it wont work & you die.

The king wants the strongest poison in the land so he can use it as an antidote, so he challenges the 2 best poisoners to a contest. Each one must bring a flask, and then they both drink from their opponents flask before drinking from their own. If their poison is the best, they will live.

However, the second best poisoner figures he can't beat the best, so comes up with a cunning scheme.
But, the best poisoner knows he is the best, and realises the second would need a cunning plan instead. So he works out what the second best was planning, and works out a counter-strategy.

On the day of the contest, the best poisoner wins.
Shortly afterwards, the king gets poisoned, tries the antidote, and dies horribly.

So...
The question is, why did the king die?

Water! Water water water!

Both poisoners just use water, so when the king gets poisoned (elsewhere), the water doesn't help him.

Damn I'm good.

edit: No wait. Then how would the best poisoner "win" if they both used water? Shit.

Mr Dom · **Posted:** Tue Jul 24, 2012 14:53

WTB wrote:

Water! Water water water!

Both poisoners just use water, so when the king gets poisoned (elsewhere), the water doesn't help him.

Damn I'm good.

But why did they both use water?
You need to show your working out!

Grim... · **Posted:** Tue Jul 24, 2012 14:54

The best poisoner made the weakest poison he could (as did the other poisoner, but he didn't make it as well).

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Mr Dom wrote:

WTB wrote:

Water! Water water water!

Both poisoners just use water, so when the king gets poisoned (elsewhere), the water doesn't help him.

Damn I'm good.

But why did they both use water?
You need to show your working out!

Well I've already buggered myself with my edit! Argh!

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Grim... wrote:

The best poisoner made the weakest poison he could (as did the other poisoner, but he didn't make it as well).

Ooh! This is interesting!

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

I know! The second best guy drank weak poison beforehand, then presented water, expecting the best poison guy to produce an awesome poison. However, he also presented water. So the second best guy dies from his initial weak poison, and the best guy just drinks two lots of water.

Mr Dom · **Posted:** Tue Jul 24, 2012 14:58

You need to work out what the original strategy is, then what the counter to that would be...

Curiosity · **Posted:** Tue Jul 24, 2012 14:59

Grim... wrote:

The best poisoner made the weakest poison he could (as did the other poisoner, but he didn't make it as well).

Then the best poisoner would have lost?

Did the poisoners come to an arrangement and fake the second best one's death?

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Mr Dom wrote:

You need to work out what the original strategy is, then what the counter to that would be...

See above!

Curiosity · **Posted:** Tue Jul 24, 2012 15:00

WTB wrote:

Mr Dom wrote:

You need to work out what the original strategy is, then what the counter to that would be...

See above!

Good shout, WTB! I liked that one

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

It was really good! I like the maths-based ones, but the "think outside the box" ones are best.

Mr Dom · **Posted:** Tue Jul 24, 2012 15:05

Huzzah!
The king is dead, long live the king, don't feed the unicorns, etc...

WTB · **Joined:** 27th Mar, 2008 **Posts:** 14497

Woo! Once again, I pass on the torch to anyone who is willing to take it... I really need to stop solving them and start finding them.

Zardoz · **Posted:** Tue Jul 24, 2012 15:22

A man finds a flea ridden cat that jumped backwards off a train.

He glues the cat into an MX-5 to take to the vets, but now he can't get into the car himself.

It takes 1 litre of warm vimto to dissolve the super glue in each lock. But he only has a 500ml bottle.

Why?

Malc · **Posted:** Tue Jul 24, 2012 15:29

Is it dimrill?

Malc

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