#math trivia #123 solution

We’ll start by assuming that single-digit numbers have their single digit in increasing order.  9 numbers so far.

Among the two-digit numbers, 36 are in increasing order:  8 in the 10s, 7 in the 20s, …, up to 1 in the 80s; 8+7+…+1 = 36.

The 100s and 200s are similar to the two-digit numbers, except that we lose the 10s in the first case and the 10s and 20s in the second.  Another 28 + 21 numbers.

In the 300s, we have just the 5 in the 40s and the 4 in the 50s.  None in the 60s, whether a leap year or not; 367 would be the first one.

Total:  9 + 36 + 28 + 21 + 5 + 4 = 103.

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