I was asked if I knew an easy way to count how many times digits occur within a range of numbers. For example in the range 10–15, how many times does each digit occur? The numbers 0, 2, 3, 4 & 5 each occur once, and 1 occurs 6 times, that is twice in the number 11, and one in every other number in the range, because the tens all start with a 1. It seemed like an odd request, but it’s for number tags on utility poles, like this one:

Electricians use these tags to identify the poles and, at least in Hungary, they’re made up of individual plates for each digit, that are screwed on to a larger plate on the pole. If you estimate too few when ordering the digits you’ll run out obviously, and if you order too many you’ll be stuck with a pile of unused digits.

It seemed like a problem that should have a simple mathematical solution to it. Unfortunately, the answers I found on Math Overflow Continue reading →