Burt Kaliski Jr. (@modulomathy)

3/25/12 10:28 AM

#math trivia for #March25: #85 is 55 base 16. How many “two of a kinds” base 16 in a leap year? (Compare #66.)

“Two of a kind” means that two of the digits are the same, base 16.

This happens 15 times from 11 to ff base 16, or up to 255 base 10.

From 100 to 16d, it’s a little more complicated because there are three digits. The patterns to count here are:

— 1xx where x is 0, or 2 through 6 (6 choices)

— 1×1 where x is 0, or 2 through 6 (6 choices)

— 11x where x is 0, or 2 through f (14 choices)

So there are 41 choices overall.

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