+1090 3!4!7! = 2n!
Divide both sides by 2:
(3!4!7!)/2 = n!
Expand the factorials:
(2 * 3 * 2 * 3 * 4 * 2 * 3 * 4 * 5 * 6 * 7)/2 = n!
Divide out the 2:
(3 * 2 * 3 * 4 * 2 * 3 * 4 * 5 * 6 * 7) = n!
Order the numbers on the left side, leaving duplicates at the end:
(2 * 3 * 4 * 5 * 6 * 7 * 2 * 3 * 3 * 4) = n!
Group the numbers at the end so that they form the succeeding numbers from the current run (current run ends at 7):
(2 * 3 * 4 * 5 * 6 * 7 * (2 * 4) * (3 * 3)) = n!
(2 * 3 * 4 * 5 * 6 * 7 * 8 * 9) = n!
Turn the left back into a factorial:
9! = n!
n! = 9!
n = 9
