Some number of pebbles are placed on a 7x7 chessboard, such that each pebble is placed inside a square and each unit square has at most one pebble. If each row and column of the chessboard contains an even number of pebbles, how many pebbles can be there be all together? (Note:- At first, the problem seemed like a piece of cake but since it appeared in an olympiad so I think it is more complicated than I think. I got the answer as 36 but I think its not true. I don't know the correct answer. Please help. )
2026-03-25 15:56:57.1774454217
A chessboard problem?
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To achieve the maximum number of pebbles, we should place the maximum number possible – 6 – in each row and column. This makes for a total of 42 pebbles, and can be done by filling in everything but a diagonal.