Evokimov

A natural number is written on the board. If you erase the last digit (in the units place), the remaining non-zero number will be divisible by 20, and if you erase the first digit, it will be divisible by 21. What is the smallest number that can be written on the board if its second digit is not equal to 0?

#
The second last digit of the number is 0, as the number without the last digit is divisible by 20. Therefore, the number must be at least four digits long. Note that the number remaining after erasing the last digit cannot be 100 according to the condition. Also, this number cannot be 120 or 140, as numbers of the form $\$$ loverline $\{20$ a $\} \$$ and \$loverline $\{40$ a $\} \$$ are not divisible by 21. For 160, there is a unique example: 1609.

## Answer

1609.