Two players alternatively erase some 9 numbers from the sequence 1,2,...,101 until only two remain. The player that starts wins x−54 dollars from the player that plays second, x being the absolute value of the difference between the remaining two numbers.

Would you rather be the first or the second player?
Explain your decision by providing your strategy.

If there are 101 numbers, and if only two are to remain at the end, then shouldn't it read this way?:

"Two players alternately erase some 99 numbers . . ."

If that is the case, then it is better to be player 2 who can cross out numbers 1 thru 49 (or 53 thru 101) which would leave x = 51 (101-50 or 52-1).

Posted by hoodat on 2017-05-24 09:36:04