In base b, there are exactly one hundred and eighty three-digit numbers whose digits are all distinct. (That's "one hundred" in the ordinary sense, 100_10.) What is b?
There are b-1 choices for the first digit, b-1 choices for the second, and b-2 choices for the third. That means (b-1)(b-1)(b-2)=180 so b=7.
:D
