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# Coins in a row

3 replies to this topic

### #1 bonanova

bonanova

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Posted 10 April 2013 - 05:29 PM

On a table is a row of fifty coins, of various denominations. Alice picks a coin from one of the ends and puts it in her pocket; then Bob chooses a coin from one of the (remaining) ends, and the alternation continues until Bob pockets the last coin.

Prove that Alice can play so as to guarantee at least as much money as Bob.
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Vidi vici veni.

### #2 BobbyGo

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Posted 10 April 2013 - 07:21 PM   Best Answer

Spoiler for

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### #3 Rob_Gandy

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Posted 10 April 2013 - 07:59 PM

Spoiler for Well

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### #4 bonanova

bonanova

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Posted 10 April 2013 - 10:00 PM

Spoiler for Well

Rob, I think this would work, because I haven't quickly found a counterexample, and it seems intuitive.

BobbyGo's answer is a proof, and got there first.

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Vidi vici veni.

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