In the summer of 1975, while I was in a Soviet math camp preparing to compete in the International Math Olympiad on behalf of the Soviet Union, my fellow team members and I were approached for help by Valera Senderov, a math teacher in one of Moscow's best special math schools.
The Mathematics Department of Moscow State University, the most prestigious mathematics school in Russia, was at that time actively trying to keep Jewish students (and other \undesirables") from enrolling in the department. One of the methods they used for doing this was to give the unwanted students a different set of problems on their oral exam. I was told that these problems were carefully designed to have elementary solutions (so that the Department could avoid scandals) that were nearly impossible to find. Any student who failed to answer could easily be rejected, so this system was an effective method of controlling admissions. These kinds of math problems were informally referred to as "Jewish" problems or "coffins". "Coffins" is the literal translation from Russian; they have also been called "killer" problems in English.
These problems and their solutions were, of course, kept secret, but Valera Senderov and his friends had managed to collect a list. In 1975, they approached us to solve these problems, so that they could train the Jewish and other students in these mathematical ideas. Our team of the best eight Soviet students, during the month we had the problems, solved only half of them. True, that we had other priorities, but this fact speaks to the difficulty of these problems.
Being young and impressionable, I was shaken by this whole situation. I had had no idea that such blatant discrimination had been going on. In addition to trying to solve them at the time, I kept these problems as my most valuable possession|I still have that teal notebook.
Later, I emigrated to the United States. When I started my own web page, one of the first things I did was to post some of the problems. People sent me more problems, and solutions to the ones I had. It turned out that not all of the cons even had elementary solutions: some were intentionally ambiguous questions, some were just plain hard, some had impossible premises. This article is a selection from my collection; we picked out some choice problems that do contain interesting tricks or ideas.