Question

Sabrina multiplied two 2-digit numbers together on the black board. Then she changed all numbers to letters (different digits changed into different letters, equal digits to equal letters.) She got AB * CD = EEFF. Prove that Sabrina made a mistake somewhere.

Answer 1

Well all I can think of is that any number with two of the same first digits and last digits like this would clearly be divisible by 11 into something where the digits would be E0F (that's a zero not the letter O) and if it's divisible by 11 then no matter what you multiply 11 by, you'll never get AB or CD since 11*A=AA or 11*B=BB if you see what I mean.