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Problem Ten: The Fifteen Game

Sep 27th, 2006 by tony

There are many pick the item math games out there, but this one is somewhat unique and has an interesting solution.

There are 9 pieces of paper on the table labelled 1 to 9. Two people take turns to pick up the numbers. Whoever has a sum of 15 first wins. What is the winning strategy? (Hint: What can you do to help you win?)

Update: Solutions have been posted.

Posted in Mathematical | 8 Comments

8 Responses to “Problem Ten: The Fifteen Game”

  1. on 27 Sep 2006 at 10:15 pm   Percy

    What happens if you go over 15?

  2. on 27 Sep 2006 at 10:28 pm   tony

    you lose

  3. on 28 Sep 2006 at 1:28 am   Sarah & Heather

    You go first, and pick up the 5. That way, no matter what they pick up, they can’t make 15, but on your 3rd try, you can always make 15.

  4. on 28 Sep 2006 at 8:31 am   tony

    I think you’re close, but they could still possibly lose. There’s a somewhat more ingenious solution.

  5. on 28 Sep 2006 at 9:20 am   Percy

    Yeah, what if:
    You pick 5
    The other guy picks 6
    You pick 9 (to prevent the other guy from winning)
    The other guy picks 1
    Now you’re at 14, and the other guy’s taken 1, so you’re forced to go over 15. :(

  6. on 28 Sep 2006 at 2:17 pm   Sarah & Heather

    haha if the other guy picks 6, you pick 4
    and then you win

  7. on 28 Sep 2006 at 5:03 pm   tony

    ok you guys pretty much got the answer but here’s the really amazing thing to notice

    Show ▼

  8. on 28 Sep 2006 at 5:17 pm   Percy

    Oh darn, I was so mistaken. I thought you individually had to get 15.

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