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10! = 10×9×8×7×6×5×4×3×2×1
= 5×2×3×3×2×2×2×7×3×2×5×2×2×3×2×1
= 7×5×5×3×3×3×3×2×2×2×2×2×2×2×2×1
So either m or n must be >= 7
= 7!×5×3×3×2×2×2×2×1
= 7! ×6×5×4×3×2×1
= 7!×6!
m=7, n=6
m×n=42

edit: how to not spoil the puzzle for others?

Nice! It’s always 42!

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And yes, 6 and 7 are one of the 3 possible answer sets. Good job!

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10, 1
10, 0

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Yes, this completes the answer sheet. 0! = 1, hence the third solution.

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OMG! You beat me by less than a minute.

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edit: how to not spoil the puzzle for others?

I suggested a feature for this yesterday: https://github.com/stackernews/stacker.news/issues/1422

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