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?

(In reply to If there isn't an even better strategy... (spoiler?) by Charlie)

You say: ....After A has reduced the set to 0 through 512, etc..

Why should he do it?, - ....after reading your answer he might chose another option which would diminish his loss, no matter what B does.

Posted by Ady TZIDON on 2015-01-22 13:09:52