ASU 010 All Russian MO 1961 9.5 game strategy
Source:
June 17, 2019
combinatoricsgame strategy
Problem Statement
Nicholas and Peter are dividing nuts. Each wants to get more. Three ways for that were suggested. (Each consist of three stages.) First two stages are common. 1 stage: Peter divides nuts onto heaps, each contain not less than nuts.
2 stage: Nicholas divides both heaps onto heaps, each contain not less than nut.
3 stage:1 way: Nicholas takes the biggest and the least heaps.
2 way: Nicholas takes two middle size heaps.
3 way: Nicholas takes either the biggest and the least heaps or two middle size heaps, but gives one nut to the Peter for the right of choice.Find the most and the least profitable method for the Nicholas.