Let abc be a 3-digit number.
Find it, if acb + bca + bac + cba + cab = 3961.

(In reply to re(2): 3 digit number by bernie)

During a preview of this problem there was some concern that nickson, our author, had made a typo. 

I think nickson had posted  " ... = 3196".   3961 was offered, but 3176 more closely fits nickson, if nickson misread his/her hand written notes.

One or two other previewers noted some other solutions, had this been a typo.

For my part I noted a place value status of a, b and c.  This formed a summation of the this 'table':
122
212
221

Now I give you:
    a*122  + b*212 + c * 221 = X

Bernie, does your reckoning fit any X where a, b & c is a single digit?

Similarly, FK, I think that I note a common 3 digit numeral shared with Bernie.   Do you both hold to the above table and its derived equation? 

I have not checked either, but I'm interested.

Posted by brianjn on 2005-10-17 08:52:59