# $$n$$-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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