Since the tiles to use are squares they can only fill in a rectangular space. 25x25 is square so the obvious problem isn't an issue.
I can only think of 3 ways that these tiles can fill in a square area:
-
using only 2x2 tiles
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using only 3x3 tiles
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or combining them into effective 6x6 tiles like so:
Next we need to look at the factors of the length of the square space. For example a 24 square space has factors including 2, 3, and 6 which means
that all 3 methods can fill in that space.
However the question's area to fill is 25x25 which only has a factor of 5 which means
that 2, 3, and 6 can never fill in the space.
Therefore the answer is:
impossible.