# A discrete mathematics problem by Áron Bán-Szabó

What is the minimum value of $$n$$, such that we are able to place one each of $$1\times 1, 1\times 2, 1\times 3, \dots, 1\times n$$ tiles inside a $$10\times 10$$ board in such a manner that we do not have sufficient space to place an $$1\times (n+1)$$ tile inside the same board?

Details and Assumptions:

• The tiles are not allowed to stick out of the board or overlap.

• We get to choose the placement of the tiles.

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