Years ago, somehow, I stumbled across a problem. Using only the digits 1-9 (not zero, and no duplications) how many combinations of nn x nnn = nnnn. You can see that it is a 2 digit number multiplied by a three digit number = a four digit number, using only the 9 digits. I have no idea what this problem was called (I presume it has a name...?) and I can`t find a reference to it. Have you heard of this one? I ended up writing a computer program to generate all the combinations and tell me the answer. Yes it`s a cheat, but there are a lot of possible combinations...:) Not many valid answers, though. Peter
Welcome to the forum. They are called alphametics or cryptarithms and can be generally solved by computer. They can also be solved by hand but would take too long for ones with multiple solutions.
There are 7 solutions to
ab x cde = fghi
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.