\(n\)-by-\(n\) grid ception?

Logic Level 4

Find the largest positive integer \(n\) that satisfies these conditions:

1. \(n\) is not divisible by \(3\).

2. The \(n\)-by-\(n\) cannot be covered by 1 I-shaped-tetromino piece and \(\dfrac{n^2-4}{3}\) I-shaped-triomino pieces.

Image of an I-shaped-tetromino:

Image of an I-shaped-triomino:

This problem is not original


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