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.

SelectClick for Answer 
The intended solution seems to be 1572 × 39 = 61308.
If we allow a fourdigit number as the first partial product, then 3598 × 12 = 43176 also works.
Yoshigahara himself passed away in 2004, so if this has a deductive solution, I’m not sure anyone knows what it is!
The problem appeared in Allan Gottlieb’s Puzzle Corner in the November/December 2012 issue of the Review, the solution in the March/April 2013 issue.
