Someone wrote down the integers from 1 to 1999 next to each other. What digit stands at the 1999th position?
There are 9 single-digit numbers, 90 two-digit numbers, and 900 three-digit numbers. The total number of digits is $9 + 2 \cdot 90 + 3 \cdot 900 = 2889 > 1999$.

This means that the 1999th digit must be found among the three-digit numbers. For the three-digit numbers, 1999 - $189 = 1810$ digits remain. $1810 = 603 \cdot 3 + 1$, which means the 1999th digit is the first digit of the 604th three-digit number, which is the first digit of 703, and this digit is 7.