Jump to content
BrainDen.com - Brain Teasers
  • 0


bonanova
 Share

Question

I have a chess board that has 13 squares on a side.

I want to break it [along the borders of the individual squares] into smaller square pieces.

I could make a 12x12 square and 25 1x1 squares - 26 in all.

I could make a 7x7 square, 3 6x6 squares and 12 1x1 squares - 16 in all.

What is the fewest I could make?

Link to comment
Share on other sites

11 answers to this question

Recommended Posts

  • 0

I can do it with 13. One 8x8, two 5x5, three 3x3, and 7 2x2. I don't know if this is the ultimate answer, but I suspect the final solution would have zero 1x1 squares.

Link to comment
Share on other sites

  • 0
12

8x8, 3- 5x5's, 2 - 3x3's, 2- 2x2's, 4- 1x1's

12 is the smallest number, although I did it with 1 7x7, 2 6x6, 1 5x5, 5 2x2 and 3 1x1 squares.

I've quickly come to learn that the next question will be: what is the optimal solution for a board of dimensions nxn, where n is odd.

(n+11)/2, for n > 3. The division consists of 1 ((n+1)/2)x((n+1)/2) square, 2 ((n-1)/2)x((n-1)/2) squares, 1 ((n-3)/2)x((n-3)/2) square, (n-3)/2 2x2 squares, and 3 1x1 squares.

Link to comment
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...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...