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# Coins in a row

Started by bonanova, Apr 10 2013 05:29 PM

3 replies to this topic

### #1

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.

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

*Vidi vici veni.*

### #2

Posted 10 April 2013 - 07:21 PM Best Answer

Spoiler for

### #3

Posted 10 April 2013 - 07:59 PM

Spoiler for Well

### #4

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.

*Vidi vici veni.*

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