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MMO 327 Moscow MO 1956 x =1/4 (a + b + c + d) infinife table

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August 19, 2019
combinatoricsmaximumtableAverage

Problem Statement

On an infinite sheet of graph paper a table is drawn so that in each square of the table stands a number equal to the arithmetic mean of the four adjacent numbers. Out of the table a piece is cut along the lines of the graph paper. Prove that the largest number on the piece always occurs at an edge, where x=14(a+b+c+d)x = \frac14 (a + b + c + d).