A trick for problem sets

Rich Pang

2026-02-23

This post is somewhat inspired by Andrej Karpathy's guide to doing well in undergrad.

Suppose your professor hands out a complex physics or mathematical problem set due in a week. How do you solve it efficiently?

The number one trick I learned in my undergrad is the following. (YMMV but I strongly doubt I am the only who will find this useful.)

Step 1: Immediately do as much as you can as fast as possible

As soon as you get the problem set do as much of it as you can in 15 minutes, or some similarly short time. Don't necessarily write out complete solutions, but chances are for some of the problems you will know roughly what approach to take but others will leave you scratching your head.

Step 2: Note precisely what the puzzles are

This is the key step. You have now split the problem set into those you know how to solve (even if you haven't yet cranked through the solution), and the head-scratchers. Identify and memorize exactly what those head-scratchers are and why they are so puzzling. If it's a typical problem set there will probably just be one or two actual head-scratchers in there, so not too much to memorize.

Step 3: Let the puzzles marinate

Instead of blocking time to work on the head-scratchers, just go about your week with them bubbling in the back of your mind. This is where the magic happens. It's quite amazing how often a solution will arise at the bus stow, while brushing your teeth, after waking up from a nap, etc. In the best case you'll solve all of the problems before you even block any significant time to work on them, and in the worst case you've only spent 15 extra minutes of your time getting a head start. It seems to me like this is a chance worth taking. True, it may be necessary to block time to work through the solution details. However, at least in my experience, when anything requires even remotely creative thinking it is far better to enlist your unconscious as an assistant. (Neural mechanism left as exercise for the reader.)

Step 4: Apply it to research

Of course, this technique is not limited to problem sets, and can be extremely useful in grad school or beyond. There the challenge is no longer solving problem sets with solutions worked out in the teacher's edition but identifying and addressing research questions at the frontiers of human understanding. Applied to research, I think this is actually quite similar to Feynman's approach, where he recommended keeping a dozen interesting problems in the back of your mind while just going around being curious about things. If the problems are bubbling around in your mind semi-continuously you massively increase your chances of recognizing a solution if one unexpectedly arises.