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

Home > Just Math
All divisible by 7 (Posted on 2008-11-04) Difficulty: 2 of 5
Imagine a rectangle divided into 3x4 squares, and put a digit in each square.
     +---+---+---+---+
     | a | b | c | d |  A
     +---+---+---+---+
     | e | f | g | h |  B
     +---+---+---+---+
     | i | j | k | l |  C
     +---+---+---+---+
       D   E   F   G
The number abcd is denoted by A, that is, A = 1000a + 100b + 10c + d, and the same for the other 2 horizontal numbers B and C.

The number aei is denoted by D, that is, D = 100a + 10e + i, and the same for the other 3 vertical numbers E, F and G.

Prove that if any 6 of these numbers (A, B, C, D, E, F, G) are divisible by 7, then the last number must also be divisible by 7.

See The Solution Submitted by pcbouhid    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Proof and Extensions | Comment 5 of 8 |
(In reply to Proof and Extensions by Steve Herman)

"I expect that this will work for any number of rows and columns, and any modulus, and any base. ".

1234
5678
9024

Modulus 2: All three horizontal numbers (still base 10) are even. Only three of the vertical numbers are even. One is odd.


  Posted by Charlie on 2008-11-06 11:47:26
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 (1)
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