Jump to content
BrainDen.com - Brain Teasers
  • 0
Sign in to follow this  
jasen

Interesting pattern on 5x5 table which has unique properties

Question

[0,1,6,4,3]
[4,5,6,0,9]
[9,9,0,1,1]
[1,0,4,5,6]
[7,6,4,9,0]

This 5x5 table has unique properties.
Each number in a cell means :

The cell = last digit of (sum of its neighbour (including diagonals))

or

The cell = The remainder of the sum of its neighbour divided by 10

Here is another example

 [0,1,6,4,8]   [1,2,1,3,2]   [1,0,9,0,1]
 [4,5,6,0,4]   [4,5,1,0,9]   [6,5,9,5,6]
 [4,4,0,6,6]   [3,3,0,7,7]   [5,5,0,5,5]
 [1,0,4,5,1]   [1,0,9,5,6]   [9,0,1,0,9]
 [2,1,4,4,0]   [8,7,9,8,9]   [4,5,1,5,4]

What surprised me is, every table like this will follow this :

  • The middle cell is always 0.
  • Any other cell (i,j), (6−i,6−j) adds upto 0 modulo 5 , that means, (i,j) + (6−i,6−j) is completely divisible by 5. 

I have checked this with my computer.

Why this happens ?

Share this post


Link to post
Share on other sites

0 answers to this question

Recommended Posts

There have been no answers to this question yet

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
Sign in to follow this  

  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...