I have found in one of the Russian high-school competitions a relatively easy puzzle & to make it more challenging replaced a certain number by N.
The modified text runs as follows:

Prove that among N sequential positive integers there always exists a number whose s.o.d. is a multiple of 11.
a. Restore N.
b. Now prove the statement.

In my free time, I like to read your blog. In coming weekend I will read  your "Eleven as mandatory divider" post.

Posted by jonemartin on 2022-11-30 02:20:35