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# First to Fifteen

Best Answer CaptainEd, 30 January 2013 - 05:06 PM

Spoiler for I would like to draw a good picture
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19 replies to this topic

### #1 bonanova

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Posted 29 January 2013 - 06:19 AM

Nine white poker chips have the numbers 1, 2, 3, ..., 8, 9 written on them, one number on each chip. You and a friend alternately select a chip, with the aim of being the first to draw three numbers that sum to 15. You may play first or second. Do you have a winning strategy?

Edited by bonanova, 29 January 2013 - 05:10 PM.
Add condition the three chips total 15 to win

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Vidi vici veni.

### #2 CaptainEd

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Posted 29 January 2013 - 03:51 PM

I'm assuming that the chips are taken out of circulation once selected.

Spoiler for my choice and strategy

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### #3 bonanova

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Posted 29 January 2013 - 04:22 PM

I'm assuming that the chips are taken out of circulation once selected.

Spoiler for my choice and strategy

Excellent.
And yes the chips are taken out of circulation once selected.

But ... I neglected to mention one other condition.
The person wins whose total is 15 after picking up three chips.

I changed the OP to include that condition.
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Vidi vici veni.

### #4 CaptainEd

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Posted 29 January 2013 - 04:35 PM

I see, I was solving a different problem anyway, thinking that we were driving the combined total to 15.

Let's see if I've got it right now.

Each person is trying to achieve his/her own total of 15. And each person has to achieve his/her sum using three chips.

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### #5 Molly Mae

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Posted 29 January 2013 - 04:54 PM

Spoiler for I (don't) have a winning strategy

Edited by Molly Mae, 29 January 2013 - 04:54 PM.

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A recipe for honey-pickled apples

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A moment in the mind is worth nine in the fire.  --Master Kilven, The Wise Man's Fear

### #6 CaptainEd

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Posted 29 January 2013 - 04:56 PM

Spoiler for now it feels like tic tac toe

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### #7 bonanova

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Posted 29 January 2013 - 05:12 PM

Spoiler for I (don't) have a winning strategy

Right. The problem properly sated is to be the first to draw three numbers that total 15.
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### #8 bonanova

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Posted 29 January 2013 - 05:13 PM

Spoiler for now it feels like tic tac toe

Ah, but the game can go beyond that point, as you note in your spoiler title.
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### #9 CaptainEd

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Posted 29 January 2013 - 05:20 PM

Spoiler for I (don't) have a winning strategy

Right. The problem properly sated is to be the first to draw three numbers that total 15.

Sorry to be dense. Is this true: I win if I am the first to have drawn M chips (M>=3), exactly 3 of which total 15?

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### #10 bushindo

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Posted 29 January 2013 - 06:02 PM

Nine white poker chips have the numbers 1, 2, 3, ..., 8, 9 written on them, one number on each chip. You and a friend alternately select a chip, with the aim of being the first to draw three numbers that sum to 15. You may play first or second. Do you have a winning strategy?

Here's a winning strategy

Spoiler for

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