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If the letters T*(RBJBR)=VPLNT each represented a unique digit, and "RBJBR" was a five digit number, what are possible values for the letters? (Or ONE possible value.)

Can we do this in a way that can be done on paper without "guessing and plugging numbers" (or computers, for that matter)?

Got this question as a math challenge from a club, not sure how do go about it.

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    Whoops, now I should go back through my questions and click those marks.2012-04-19

1 Answers 1

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Here is a start...

If you check the last digit, you'll see that $T*R$ ends in $T$. Also, by looking at the first digit, $T*R$ is at most $9$, otherwise the right side has $6$ digits.

Then $T*R=T$ which means that either $T=0$ (not possible) or $R=1$. Thus $R=1$.

$T*(1BJB1)=VPLNT$

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    which reduces the problem to $T\cdot(1BJB)=VPLN$.2012-04-19