An integer N consisting of five distinct nonzero digits has the curious property that it is equal to the sum of all the different three-digit integers formed by the three digit permutations of its five digits. Find N.

I wrote a code comparing the sum of all 60 combinations of a five digit number to (a*10000)+(b*1000)+(c*100)+(d*10)+e, where a,b,c,d,e increments as needed to count up.

There were a LOT of 5 digit intgers that fit this, but they all seemed to have duplicated digits - multiple 1's and 2's at first.

The first number it presented that didn't duplicate any of the digits was 12543 (or somewhere around there. I forgot to write it down last night). It was 12 thousand something.

So, there are a bunch of N's. And seems to be quite a few where no digits are duplicated.

Posted by Jim on 2004-07-16 11:46:55