If we want to write down all the integers from 1 to 10,000, how many times do we need to write a digit, for example, the digit 5?
A certain digit appears 1000 times in the units place up to 10,000, 10 times in every hundred group in the tens place, which is 1000 times in total, 100 times in every thousand group in the hundreds place, also 1000 times in total, and 1000 times in the thousands place. Therefore, we have to write a digit 4000 times if we want to write down the numbers from 1. The 0 is not written as many times, as we write it 9 times as a ten, 99 times as a hundred, and 999 times as a thousand, so we have to write the $0$ a total of 2893 times.

(Paunz Rezsó, Pécs.)