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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