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

Arrange the numbers 1 to 19 in the circles

Question

     O---o---O
    / \     / \
   o   o   o   o
  /     \ /     \
 O---o---O---o---O
  \     / \     /
   o   o   o   o
    \ /     \ /
     O---o---O

Arrange the numbers 1 to 19 in the circles, so all the rows of 3 numbers between O (big o) sums to 23

Example :

     a---b---c
    / \     / \
   d   e   f   g
  /     \ /     \
 h---i---j---k---l
  \     / \     /
   m   n   o   p
    \ /     \ /
     q---r---s

a+b+c = a+e+j = c+f+j = 23, and so on....

Note :

  • There are 2 solutions, if we rule out reflections and rotations.

Bonus Puzzle : How if all the rows of 3 numbers between O (big o) sums to 22,24,25,26,27,28,29,31,32,33,34,35,36, 37, and 38. I have checked all the solutions by computer, and all those sums have solutions.

Edited by jasen

Share this post


Link to post
Share on other sites

1 answer to this question

Recommended Posts

  • 0

 

Spoiler

1,19,3,12,16,14,18,10,7,6,15,2,5,9,13,17,8,11,4

1,19,3,18,16,14,12,4,13,6,9,8,17,15,7,5,2,11,10

Set a, b, and c to 1, 19, and 3 to constrain the only way 19 can fit with the requirements. Used excel to solve for the remaining corners and center.

 

Share this post


Link to post
Share on other sites

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...