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

Home > Numbers
Adjacently Greater Than One (Posted on 2010-01-01) Difficulty: 2 of 5
Determine all possible values of a 6-digit positive integer N having 6 different digits from 0 to 9, with the first digit being nonzero, such that:

(i) Either, the digits at the even positions are even and the digits at the odd positions are odd – or, the digits at the even positions are odd and the digits at the odd positions are even. Zero is regarded as an even digit.

(ii) The absolute difference between two adjacent digits is always greater than one.

(iii) The 2-digit number formed by the first and second digit as well as the 2-digit number formed by the third and fourth digit is divisible by the 2-digit number formed by the fifth and sixth digit.

  Submitted by K Sengupta    
Rating: 3.3333 (3 votes)
Solution: (Hide)
Forbidding leading zeroes from two digit numbers, the only solution is:903618.

Allowing leading zeroes to 2-digit numbers, there are4 4 further solutions. These are: 496307, 692703, 816309, and 816903.

For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionA computer program listing and spoilerCharlie2010-01-01 14:01:25
re: Computer Solution- disclaimerAdy TZIDON2010-01-01 13:54:11
re(2): SPOILER- errare humanum estAdy TZIDON2010-01-01 13:51:57
Computer SolutionJim Keneipp2010-01-01 13:37:59
re: SPOILERCharlie2010-01-01 13:13:53
SolutionSPOILERAdy TZIDON2010-01-01 12:20:12
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (1)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information