A Moscow Math Circle Week By Week Problem Sets Msri Mathematical Circles Library

Getting Started With Week By Week Problem Sets From the Moscow Math Circle Program

I picked up A Moscow Math Circle Week By Week Problem Sets Msri Mathematical Circles Library because the traditional textbooks weren't hitting the right difficulty level for the kids I was working with. The MSRI Mathematical Circles Library series has some solid titles, but Moscow's approach stands apart in how it structures practice over a full academic year rather than dumping problems by topic. The collection covers roughly 34 weeks of material, organized into themes like combinatorics, geometry proofs, number theory basics, and logical reasoning. Each week typically has 4-8 problems ranging from warm-up level to competition-level challenges. The answer key is at the back, but solutions are sparse. You're expected to work through proof logic yourself or guide students toward it rather than handing them a completed argument. The problem progression is deliberate. Week 1 through 6 introduce counting strategies and simple pigeonhole principle applications. Weeks 7 through 12 move into parity arguments and invariant thinking. The geometry section doesn't start until around week 18, which caught me off guard on my first run-through. I had assumed the structure would be more thematic. It's chronological instead, and each week builds on techniques introduced earlier rather than starting fresh each time.

How I use it in practice

I run a Saturday morning math circle with about twelve kids, ages 10 to 13. I print one week's set at a time. The kids work individually for the first twenty minutes, then we discuss as a group. The problems are designed so that every student can attempt at least the first two or three, even if they only solve one completely. The harder problems at the end of each set usually require insight that comes from the easier ones. One thing that isn't obvious: the books assume a certain baseline comfort with reading mathematical statements. If your group hasn't seen basic proof language before, you'll spend extra time just translating problem statements into terms they understand. I usually pre-teach vocabulary on the board before handing out the sheet. Things like "congruent," "contradiction," and "without loss of generality" come up frequently and cause hesitation if they're unfamiliar.

Issues I ran into and how I fixed them

My biggest friction point was that some problems reference figures or diagrams that aren't clearly described in text. Week 23, problem 4 about tiling a modified chessboard needs you to visualize the board, and the printed version only says "remove two opposite corners." I ended up drawing the board on the whiteboard each time rather than trying to make them picture it from words alone. This took about two extra minutes per problem but saved a lot of confusion. Another thing: the difficulty jump between weeks 28 and 29 is steep. I found two students who had been keeping up suddenly stuck at week 29, which involves a more sophisticated application of the pigeonhole principle across multiple dimensions. I went back to week 26 problems with them and reworked the explanation before returning to week 29. They caught up within two sessions. Don't power through this gap.

Who should use this and who shouldn't

This works well for a guided math circle setting where an adult can facilitate discussion. It's not really designed for independent study at home, though motivated students can manage it with the back-of-book answers. If you're looking for a self-contained curriculum with full worked examples, this isn't it. You'll need to supplement with your own explanations or pair it with something like Mathematical Circles by Karpovich et al. for additional context. The resource is available through the MSRI store and Amazon. Physical copies tend to run between $25 and $35 depending on the seller. Digital versions exist on some third-party sites but aren't officially distributed. I'd recommend the print edition. The paper quality is decent and it lays flat, which matters when you're marking up problems with a pen during a session.

A few practical notes

If you're using this with a group, I suggest printing only the problem pages, not the full document with answers included. It's easy enough to keep the original and photocopy what you need. The pacing works best at one set per week. Trying to rush through two weeks' material in one sitting usually means the students absorb less from each problem. The whole point of the week-by-week structure is repetition of underlying techniques across different problem types, and compressing it undermines that design.