Congratulations to Steve Everson, who won a copy of “The Simpsons and Their Mathematical Secrets” by correctly deciphering:
DAVID x COHEN= 763860049
13241 X 57689 = 763860049
He summarised his method as: “Started from the lowest digit (there is only one assignment for D and N that works) and worked my way up.”
In other words, obtaining 9 as the final digit of the product means that the final two digits of DAVID & COHEN have to be 3 & 3, or 7 & 7, or 1 & 9, or 9 & 1. However, 3 & 3 and 7 & 7 cannot be correct, as the digits have to be different. Similarly, 9 & 1 cannot be correct, because if D=9 then it both ends and starts with a 9, and you that would force COHEN to be a 4-digit number, when it has to be a 5-digit number – does that make sense?
Once you have got as far as 1AVI1 x COHE9 = 763860049, then you can pick away at the rest of the number.
Alternatively, I know that some people used a brute force computer search approach. Moreover, some guessed that the solution might be a pair of primes, which made searching much easier.