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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? 

 Dec 30, 2020
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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

 Jan 7, 2021

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