All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
Sum number equals integer (Posted on 2011-06-11) Difficulty: 3 of 5
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.

                              (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    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts A start, | Comment 1 of 5
There are 9 letters used: numberitg so x is at least 9.

Since x is the base we can distribute (x-1)*number = number0-number = integer or


r+r ends in 0 so either r is zero or it is half the base and this base must be even.  If r is zero e+e ends in zero so e is half the base and the base must be even.  [either way the base is even]  If r is not zero, r+r has a carry so for e+e to end in r, r must be odd.


n+n gives a carry so n is at least half the base.  I can't be half the base (e or r is) so it is at least one more than half the base and n is at least two more than half the base.

I probably will not be able to derive all that much more, but if nothing else this speeds up a computer search.

  Posted by Jer on 2011-06-14 02:03:15
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information