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.
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!