perplexus.info :: Numbers : Sum number equals integer

Sum number equals integer (Posted on 2011-06-11)

Each of the small letters in bold represents a different base x digit from 0 to x-1 to satisfy this alphametic equation. None of the numbers can contain any leading zero.

牋牋牋牋牋牋牋牋牋牋牋牋牋牋牋(x-1)*number = integer

Determine the minimum positive integer value of x such that the above equation has at least one solution. What is the next smallest value of x having this property?

No Solution Yet Submitted by K Sengupta

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Nice start

| Comment 2 of 5 |

Nice start, Jer.

One stray observation, which may or may not be useful, is that the left side of the equation = 0 (mod x-1)

This means that the right side also = 0 (mod x-1).

By casting out x-1's, this means that

(I + n + t + e + g + e + r) = 0 mod (x-1)

Posted by Steve Herman on 2011-06-14 21:20:01

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