Just offering this as a curiosity:

It was devised by the late Japanese cryptogramist Kyoko Ohnishi, and praised by puzzle maven Nob Yoshigahara. If each letter stands for a unique digit, what product is encoded here?

When this appeared in MIT Technology Review in November 2012, it attracted 20 responses, but it appears that all of them used computers to find the solution. If there’s a way to reason it out, I don’t think anyone has found it yet.

If we assume that neither of the factors has a leading zero, and that the partial products have five and four digits, as shown, then the solution is unique. I’ll put it in the spoiler box below, in case you want to work on it yourself.