Introduction: Here is a problem that I think would be good for any child who knows how to use the standard algorithm to do multi-digit multiplication. It is a cryptarithm from The Moscow Book of Puzzles, an amusing book by Boris Kordemsky, available in a very inexpensive Dover edition. For those of you who don't know (as I didn't) a cryptarithm is like a cryptogram, except the unknowns are digits, not letters. One you may have seen is (S E N D) + (M O R E) = (M O N E Y), where each letter stands for a digit, with different letters standing for different digits, and the expressions in parentheses standing for multi-digit numbers.
Problem: In the following multiplication, each * stands for a prime number digit (2, 3, 5, 7). Replace each * by a prime digit so that the multiplication is correct.
* * *
x * *
* * * *
* * * *
* * * * *
Strangely enough, you have all the information you need to find the unique solution.