RU-ALLRUSSIAN 1961 Problem 10
- Answer
A and B play the following game with N counters. A divides the counters into 2 piles, each with at least 2 counters. Then B divides each pile into 2 piles, each with at least one counter. B then takes 2 piles according to a rule which both of them know, and A takes the remaining 2 piles. Both A and B make their choices in order to end up with as many counters as possible. There are 3 possibilities for the rule:
B takes the biggest heap (or one of them if there is more than one) and the smallest heap (or one of them if there is more than one).
B takes the two middling heaps (the two heaps that A would take under ).
B has the choice of taking either the biggest and smallest, or the two middling heaps. For each rule, how many counters will A get if both players play optimally?
Dataset text NuminaMath olympiads. Quoted with source.
Show the answer
[N/2], [(N+1)/2], [N/2]
Solutions
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