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

Home > Numbers
No direct evaluation (Posted on 2015-06-09) Difficulty: 2 of 5
Given that 2^29 is a nine-digit number all of whose digits are distinct, determine which of the ten digits is missing.
Provide your answer without computing the actual number.

Source: SMO contest

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 2 of 4 |
(In reply to Solution by Jer)

your answer is right but I must disagree with your reasoning as stated.  It needs to be clarified that this approach only works if the number has a non-zero digital root.


For example, take the 9-digit number 102345678.  It has 9 distinct digits which sum to 36 which is a multiple of 9 thus
102345678 = 0 mod 9
however the missing digit is not zero

so in general
if N is a 9-digit number consisting of 9 distinct digits, then
N= r mod 9
means that r is the missing digit UNLESS r=0 in which case the missing digit could be either 0 or 9

  Posted by Daniel on 2015-06-09 09:43:07
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information