RU-ALLRUSSIAN 1971 Problem 3
- Answer
(1) Player A writes down two rows of 10 positive integers, one under the other. The numbers must be chosen so that if a is under b and c is under d, then a + d = b + c. Player B is allowed to ask for the identity of the number in row i, column j. How many questions must he ask to be sure of determining all the numbers?
(2) An m x n array of positive integers is written on the blackboard. It has the property that for any four numbers a, b, c, d with a and b in the same row, c and d in the same row, a above c (in the same column) and b above d (in the same column) we have a + d = b + c. If some numbers are wiped off, how many must be left for the table to be accurately restored?
Dataset text NuminaMath olympiads. Quoted with source.
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m+n-1
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