Folklore

The numbers $4,14,24, \ldots, 94,104$ are written on the board. Is it possible to erase one number from those written, then erase two more, then three more, and finally four more numbers so that after each erasure the sum of the remaining numbers on the board is divisible by 11?
Note that the 11 even numbers written down form an arithmetic progression, so their sum is divisible by 11. Therefore, in order for the sum of the remaining numbers to be divisible by 11 after the first erasure, it is necessary to erase a number that is a multiple of 11. Moreover, after four erasures, one number should remain, which is again a multiple of 11. However, among the written numbers, only one number (44) is a multiple of 11. Thus, it is impossible to perform the specified operations.

## Answer

It is not possible.