#math trivia #122 solution

All of the one-digit day-numbers, 1-9, when reversed, are themselves, so have the property.  That’s 9.

All of the two-digit day-numbers, 10-99, when reversed, are also day-numbers, except that those ending in 0 aren’t allowed (i.e., their reversal isn’t).  That’s another 81.

It gets more complicated with the three-digit day-numbers.

Let’s start by excluding the day-numbers that end in 0, or 4 or larger.  This leaves the following:

  • 10x – 36x, where x is 1, 2 or 3

All of these when reversed are also day-numbers.  That’s another 27*3 = 81.  So we have 171 overall.

It’s a nice coincidence that there are 81 two-digit numbers and 81 three-digit numbers in the set.  If any three-digit number were allowed, not just day-numbers between 1 and 366, then there would be 810 three-digit numbers in the set, or 900 overall.  The number of possibilities for a fixed number of digits roughly increases with the square of the upper bound.

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