## Which coin?

A forum for good logic/math puzzles.

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Joined: Mon Apr 27, 2009 12:39 am UTC

### Which coin?

Having been convicted of gambling, you step forward over the hardwood floor to the judge's table in order to receive your sentence. He puts down his glass of water and hands you two pennies. One of them is unmodified, the other has been bent into a shallow cup, with heads on the inside and tails on the outside. He says:
"Choose one of these coins, and flip it. If it lands on heads, you are free. If it lands on tails, you will be executed at dawn."
Which coin should you flip to maximize your chance of survival?
I... I didn't do it.
<- he did it, I swear

gcoope
Posts: 30
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### Re: Which coin?

Spoiler:
Flip the bent coin into his water?

Posts: 192
Joined: Mon Apr 27, 2009 12:39 am UTC

### Re: Which coin?

Spoiler:
Well, that was over quickly.
I... I didn't do it.
<- he did it, I swear

t1mm01994
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Location: San Francisco.. Wait up, I'll tell you some tales!

### Re: Which coin?

Ironic, how you have to gamble your life if you are convicted to death because of gambling...

Posts: 1
Joined: Fri Dec 26, 2008 1:46 am UTC

### Re: Which coin?

Spoiler:
the bent coin.

The bent coin has a slightly stretched tail's face. On the last bounce (of the tossed coin), when the coin is in contact with the board, any point on the slightly stretched face will cushion the fall and roll it towards having the tail facing down. With that, the heads will face up.

RonWessels
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Location: Mississauga, ON, CA

### Re: Which coin?

Spoiler:
I agree that it's the bent coin, but with different reasoning.

The bent coin has its center of gravity offset towards the tails side, thereby biasing it to fall tails-down.

jaap
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### Re: Which coin?

I'm not so sure the reasoning in the previous two posts is the whole story.
Spoiler:
If the bent coin is spinning when it hits the table, landing on the curved side will not slow its spinning as much as landing on the hollow side. This may cause it to roll over onto the other side more often.
This is similar to a cubical die on which the edges around one face are a bit more rounded than the others, so causing it to roll away from that face more easily giving it a worse than 1/6 probability.
As to whether this effect dominates or not, I have no idea.

Moose Hole
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### Re: Which coin?

He says flip, not toss, so he could just turn the coin over and be following instructions. In that case, he should choose a coin that currently has the wrong outcome.

Elvish Pillager
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### Re: Which coin?

It's obviously
Spoiler:
A trick. The judge said "lands on heads", which arguably means lands with the heads face-down. But if you point that out, the judge has plausible deniability and can get you either way.

So what you need to do is get a bucket full of frog heads, and flip a coin into it. It doesn't matter which one. Then nobody can argue the coin didn't land on heads.
Also known as Eli Dupree. Check out elidupree.com for my comics, games, and other work.

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Age of Fable
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### Re: Which coin?

Spoiler:
What happens if the bent coin lands with heads downwards? It could be argued to have landed on an edge, not 'on heads'.
Teleleli The people, places, gods and monsters of the great city and the islands around.

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### Re: Which coin?

Spoiler:
It's a test. Don't flip either, look the judge in the eye, and, with a cracking, yet vaguely proud voice, say, "Your honor, after what happened the last time I gambled, I swore I would never- NEVER - gamble again. Though it will be the death of me, I will not break my promise."