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

 Sum To 2007 Nines? (Posted on 2007-10-15)
The number N is obtained by rearranging the digits of a positive decimal whole number M.

Can M+N be equal to 99.....9, where the digit 9 is repeated precisely 2007 times?

 See The Solution Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 hint | Comment 1 of 11
The rightmost digit of M plus the rightmost digit of N can't exceed 18, so these two digits must add up to 9, with no carry.  The same applies to the digits to the left of these.  So there is no carry taking place in any of the place positions.

Thus M and N each have 2007 digits-- an odd number.

Another way of showing that is that the leftmost digit of the total is not a 1, also leading to M and N each having 2007 digits.

Edited on October 15, 2007, 2:49 pm
 Posted by Charlie on 2007-10-15 14:45:05

 Search: Search body:
Forums (0)