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numbers 1-24 on faces 2x2x2 cube All-Russian MO 2005 Regional 9.3

Source:

August 26, 2024
combinatorics

Problem Statement

Two players take turns placing the numbers 1,2,3,...,241, 2, 3,. . . , 24, in each of the 2424 squares on the surface of a 2×2×22 \times 2 \times 2 cube (each number can be placed once). The second player wants the sum of the numbers in each cell the rings of 88 cells encircling the cube were identical. Will he be able to the first player to stop him?
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