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

Home > Numbers
Magic Sum (Posted on 2005-09-22) Difficulty: 2 of 5
Someone fills a 6x6 matrix with the numbers from 1 to 36 first across, then down, like:
 1  2  3  4  5  6
 7  8  9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
Now they ask for volunteers to randomly select numbers. The number selected will be circled and the others in the same row and column will be crossed out. Non-crossed out numbers are selected until no more numbers can be chosen. For example, selecting 8 means that 7, 9, 10, 11, 12, 2, 14, 20, 26, and 32, can no longer be chosen.

When all is said and done, the total of the circled numbers is 111.

Can you prove why this is so?

To give credit where due, I first saw this on curiousmath.com

See The Solution Submitted by Bob Smith    
Rating: 3.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 2 of 6 |
 
An element of the array is A(I,J) = 6(I-1)+J.
There is only one circled element in each row
and column. Summing the element in each row:
  Row  Element
   1     0 + J_1 +
   2     6 + J_2 +
   3    12 + J_3 +
   4    18 + J_4 +
   5    24 + J_5 +
   6    30 + J_6 
     =  90 + (J_1 + J_2 + J_3 + J_4 + J_5 + J_6)
     =  90 + 21
     =  111      
  

  Posted by Bractals on 2005-09-22 02:57:49
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 (8)
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