Jump to content

Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse

- - - - -

Killing squares

  • Please log in to reply
1 reply to this topic

#1 bonanova



  • Moderator
  • PipPipPipPip
  • 6161 posts
  • Gender:Male
  • Location:New York

Posted 05 April 2013 - 09:18 PM

Forty toothpicks form a 4x4 checkerboard as shown in the figure.

What is the smallest number of toothpicks that if removed will break

the perimeter of every square: the 16 unit squares, the 9 order-2 squares,

the 4 3x3 squares and of course the outside border?


If you like, extend the problem to

  1. prove your answer is smallest possible.
  2. destroy every rectangle (including the squares) with fewest removals.
  3. extend the size of the square to 5x5, 6x6, 7x7 and 8x8.
  4. derive an expression for the fewest removals.

  • 0

Vidi vici veni.

#2 k-man


    Senior Member

  • Members
  • PipPipPipPip
  • 537 posts
  • Gender:Male

Posted 05 April 2013 - 10:23 PM

Spoiler for #1

  • 0

0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users