# Algorithm (cryptarithm) question, yes it is homework, but I can't get it

The following is a multiplication problem in traditional base ten notation. Each letter represents a different digit. What digit does each letter represent? How did you get your foot in the door?

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could x and y both be 0 –  NEWprogrammer Dec 3 '10 at 0:03
what is the fraction in the fourth line for? –  Timothy Wagner Dec 3 '10 at 0:05
i posted the way it looks in the book –  NEWprogrammer Dec 3 '10 at 0:09
OK, it wasn't clear from the way you wrote it. –  Timothy Wagner Dec 3 '10 at 0:16

For the first equation $X=1,Y=0$ works.

This should be the only solution since, $XY\cdot YX= XY$ implies $XY=0$ or if $XY\neq 0$ then, $YX=1$. If $XY=0$ then $X=Y=0$ (remember $X,Y$ are digits here), so they are not distinct.

For the second part, $Y=0$, so the only way to get a third digit in the final solution, would be to have $X+Z=1+Z$ be a two digit sum. This can only happen if $Z=9$, so $V=0$ and $W=1$

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that would give be 10*01=10, so that works –  NEWprogrammer Dec 3 '10 at 0:04
how in the world did you even figure this out –  NEWprogrammer Dec 3 '10 at 0:17
try a few and you'll learn all the tricks. –  Yuval Filmus Dec 3 '10 at 5:14