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Problem 5...................................(just to reach minimum character limit)

Problem 5...................................(just to reach minimum character limit)

Question Image
Grade:12

2 Answers

mycroft holmes
272 Points
4 years ago
Part (a) is simple to disprove. Just arrange the numbers 64, 63,...,57 along the diagonal in descending order (i.e. 64 in a1,1, 63 in a2,2,..., 57 in a8,8). That way there will be no interesting number.
mycroft holmes
272 Points
4 years ago
Part (b) Suppose p and q are two such numbers that are interesting in row r and s resp. WLOG p>q
 
Consider p in row s and in the same col as p. Then q>p’>p which is a contradiction. Hence at most 1 interesting number can be there.

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