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At the carnival, I stroll towards the beer garden when one of the games caught my eye. It has a board with the numbers 1 through 9 laid out in a row. When I ask about it, the game owner ticks off the rules:

We take turns placing money on one of the numbers, with me going first. I will place 1-dollar bills, he will place 5-dollar bills. Each number can be used only once. If I hit on three numbers adding up to 15 before the owner, I take all the money on the board winning his 5-dollar bills. If he gets 15 first, he gets all the money and I lose my 1-dollar bills. If neither succeeds, all money is returned.

I am suspicious of the odds, but I tactfully accept as I think about what secrets he has in tow to avoid losing all that money. Perhaps he is hiding something by laying the numbers out in a row rather than a 3×3 square.

If I suspect he never loses, how should I play to at least force a tie?

Bonus: The owner makes me an offer: If I let him go first so he gets five numbers and I get only four, he will give me 2 dollars for a tie. Should I take him up on this offer?

There are hidden hints in the problem statement, a favorite tactic of mine.

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    $\begingroup$ Looks a lot like this $\endgroup$
    – Lezzup
    Commented Oct 14 at 13:12

1 Answer 1

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Imagine the numbers arranged in an 3x3 magic square instead of a straight line. For example:
2 7 6
9 5 1
4 3 8
Every column, row and diagonal sums up to 15. Now you can play TicTacToe on this square and use the same strategies.
Assuming both players playing optimally the game always ends in a tie. So for the bonus you should accept the offer.

Some hints I spotted:

the game owner ticks off the rules - like in TicTacToe
Perhaps he is hiding something by laying the numbers out in a row rather than a 3×3 square. - very obvious
I tactfully accept as I think about what secrets he has in tow - again like in TicTacToe

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  • $\begingroup$ So did you see where my hints are? :-) $\endgroup$
    – Oscar Lanzi
    Commented Oct 14 at 13:01
  • $\begingroup$ I added some hints i spotted in an edit $\endgroup$
    – inkili
    Commented Oct 14 at 13:06
  • $\begingroup$ I also use the word "rltactic". More subtly: I am strolling towards the beer "garden" — I got this from Martin Gardiner! $\endgroup$
    – Oscar Lanzi
    Commented Oct 14 at 13:09
  • $\begingroup$ Maybe so, but the carnival format is what I first saw. I couldn't figure out where to look for a duplicate. $\endgroup$
    – Oscar Lanzi
    Commented Oct 14 at 13:14
  • $\begingroup$ @OscarLanzi, the core of this game is '15' and 'cards'. If you search '15 cards', or even '15 cards sum', you'll find the other questions pretty easily. $\endgroup$
    – Lezzup
    Commented Oct 14 at 13:23

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