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What price glory? (Posted on 2015-01-22) Difficulty: 2 of 5
Two math. wizards play in the following manner:
From a row of integers 0,1,2,…1023,1024 A erases 512 numbers of his choice, - following this B erases 256 numbers of B’s choice.
Step 3: A erases 128 numbers, etc…
So at Step 10 player B chooses one of the 3 remaining numbers and erases it to define the amount of (dollars, pounds, euros, marbles) to be paid by A i.e. the difference between the two remaining numbers.

Clearly, A chooses a strategy to minimize this amount while
his opponent wants to maximize the outcome.

Assuming both follow the best strategy (Which?),
what will be the outcome of the game?

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: If there isn't an even better strategy... (spoiler?) | Comment 2 of 5 |
(In reply to If there isn't an even better strategy... (spoiler?) by Charlie)

I agree with your optimum strategy.

A doesn't seem to have a better way.  I tried having A leave clusters of numbers, knowing he can remove them later, but since numbers diminish quickly he can't remove enough.

B can use cluster strategies but at best they seem equal to the "take every other" strategy.

  Posted by Jer on 2015-01-22 12:02:31

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