The equation n! = 6! × 7! relates three factorials. How large is n?
The equation can be written as n! = 7! × 6!
= 7! × 1 × 2 × 3 × 4 × 5 × 6
= 7! × 2 × 3 × 4 × 5 × (2 × 3)
= 7! × (2 × 4) × (3 × 3) × (2 × 5)
= 7! × 8 × 9 × 10
= 10!
Therefore, n = 10.
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This puzzle originally appeared in Spektrum der Wissenschaft and was reproduced with permission.