I like the idea of different bases for later on in the unit. I prefer to begin by doing a lot in base 10 (other than the job of translating between an exponential statement and a logarithmic statement) because I want to build intuition for why log(3) is a bit less than 1/2 and log(2) is a bit less than 1/3 and so on. This game really helps with that!

]]>A couple of variations that spring to mind:

* play with a pair of dice, and say “you can use either the total or the two dice separately” — although this may diminish the log(1) pain!

* play with bars in different bases (e.g. from 2 up to 12), with different numbers of points for each.

The next place to go is to restrict player 1’s choice of numbers. For instance, what if they have to choose from 1 through 10, without replacement? In other words, they can have at most 5 odds. Can they still win? A lot of your strategies so far won’t work any more, but maybe there are other ways to win.

There’s some good discussion over on the Numberplay blog’s comments too.

]]>1 x, 1 () : Gotta think this one out more.

BTW — I really like how this problem is evolving, Josh. Thanks for bringing it to my attention!

]]>What about exactly 2 x’s?

What about exactly one x, and one set of parentheses?

]]>For no x’s : Player 1 wins by choosing 7 odds and an even.

For 0 or 1 x’s: Player 2 wins by choosing no x’s (if that works) or by placing an x between an odd and an even.

For exactly 1 x: Player 1 wins by choosing 8 odds. (this also works if Player 2 must use an odd number of x’s.

]]>Cool puzzle, Josh — I am curious to see where it ends up going. ðŸ˜‰

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