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10 replies to this topic

### #1 phillip1882

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Posted 01 August 2010 - 03:26 AM

a group of 16 men each have a hat numbered 1-8, repeats allowed. the need to communicate their hat number by way of shaking hands. if a hand shake is accepted, it is counted against both players. if rejected, it doesn't hurt either of them. what's the fewest number of accepted hand shakes you would need for everyone to determine their hat number? which player has the best chance of winning?

Edited by phillip1882, 01 August 2010 - 03:28 AM.

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### #2 bonanova

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Posted 01 August 2010 - 05:05 AM

What do players learn from an accepted or rejected handshake?
Is there a strategy agreed upon before this process starts?
Or is that all part of the puzzle?

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Vidi vici veni.

### #3 qwe qwe

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Posted 01 August 2010 - 05:29 AM

I think they should agree on a strategy first, here's my attempt:

You didn't say that each number is repeated exactly once so I take it that any number can appear from 0 to 16 times?

Spoiler for

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### #4 Dej Mar

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Posted 01 August 2010 - 07:11 AM

a group of 16 men each have a hat numbered 1-8, repeats allowed. the need to communicate their hat number by way of shaking hands. if a hand shake is accepted, it is counted against both players. if rejected, it doesn't hurt either of them. what's the fewest number of accepted hand shakes you would need for everyone to determine their hat number? which player has the best chance of winning?

The puzzle is not clearly defined. Whose hat number does each man need to communicate --
their own or each of the other 15 men?
Do the 16 men know their own hat numbers?
Can they see the other men's hat numbers but not their own?
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### #5 viola117

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Posted 01 August 2010 - 05:53 PM

a group of 16 men each have a hat numbered 1-8, repeats allowed. the need to communicate their hat number by way of shaking hands. if a hand shake is accepted, it is counted against both players. if rejected, it doesn't hurt either of them. what's the fewest number of accepted hand shakes you would need for everyone to determine their hat number? which player has the best chance of winning?

Spoiler for My answer, if they are allowed to make a strategy.

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### #6 Arbelle

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Posted 01 August 2010 - 06:12 PM

Spoiler for There is a good chance I didn't understand the rules, but

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### #7 phillip1882

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Posted 01 August 2010 - 07:00 PM

yes they can form a strategy before hand and yes they can see everyone else's hat number but not their own.
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### #8 mmiguel1

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Posted 01 August 2010 - 08:04 PM

Spoiler for

Edited by mmiguel1, 01 August 2010 - 08:06 PM.

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### #9 mmiguel1

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Posted 01 August 2010 - 08:07 PM

Spoiler for

I just read Arbelle's which is much more elegant than mine. I like that way better.

Edited by mmiguel1, 01 August 2010 - 08:09 PM.

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### #10 Dej Mar

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Posted 01 August 2010 - 11:12 PM

Spoiler for No need for a secret club handshake.

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