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Stacking rectangles

Combinatorics Level 3 90 points

Given a 100 by 100 square grid, what is the largest number of 1 by 51 rectangles that we can cut out of it?

Details and assumptions

Clarification: The rectangles are cut directly out of the grid, so you may not 'reuse' the unit squares. You may not 'glue' or 'paste' the unit squares together after cutting.


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