In the following cryptarithm, each letter represents a distinct digit (base 10):

. . . . .

Identify the digits.

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- December 29th 2006, 07:34 AMSorobanQuickie #5
In the following cryptarithm, each letter represents a distinct digit (base 10):

. . . . .

Identify the digits. - December 29th 2006, 03:31 PMOReilly
- December 29th 2006, 04:48 PMSoroban
Hello, OReilly!

Your solution is correct.

You offer no explanation . . . did you use some software?

- December 29th 2006, 07:09 PMgalactus
Hey Soroban:

I scratched my head on this one for a while.

One could tackle this in many ways, but if we let FRY=f and HAM=h, then

we can whittle it down to something easier to solve.

Then we have:

. Divide through by 13.

Now, the ol' switcharoo.

I was amazed this actually worked.

I didn't see the very last part right away.

Because we can switch them around and have 538461 and 461538

- December 30th 2006, 02:08 AMearboth
Hello Soroban,

your problem needs "nothing else" but counting. So I wrote a small program (see attachment) and the result popped up rather immediately. There isn't any mathematical thinking or deduction involved so I didn't dare to publish my "solution". so this post is only for the records.

EB - December 30th 2006, 03:21 AMSoroban
Lovely, Galactus!

That is*exactly*the Quickie solution.

Punchline: .Your final equation was: .

Since and are relatively prime (you already divided out the GCD),

. . the only solution in positive integers is: .

- December 30th 2006, 06:18 AMgalactus