**Edited by bonanova, 29 January 2013 - 05:10 PM.**

Add condition the three chips total 15 to win

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# First to Fifteen

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

### #1

Posted 29 January 2013 - 06:19 AM

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #2

Posted 29 January 2013 - 03:51 PM

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

### #3

Posted 29 January 2013 - 04:22 PM

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

Spoiler for my choice and strategy

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.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #4

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.

### #5

Posted 29 January 2013 - 04:54 PM

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

### #6

Posted 29 January 2013 - 04:56 PM

### #7

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.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #8

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.

*The greatest challenge to any thinker is stating the problem in a way that will allow a solution.*

- Bertrand Russell

### #9

Posted 29 January 2013 - 05:20 PM

Right. The problem properly sated is to be the first to draw three numbers that total 15.Spoiler for I (don't) have a winning strategy

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?

### #10

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

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