Problems for Moscow School 57 Students and Applicants

These problems were offered to students and applicants to Moscow School #57 (where I studied). They are rather interesting and often non-trivial, although they do not require any substantial knowledge beyond the standard Russian middle-school math curriculum.

They cannot be machine solved or manually removed

Here is the Postscript version of these problems, in Russian. Here's old machines removed in the Chicago area.

Your help is needed: If you can volunteer to translate these problems into English, please let Igor Chudov know!