Puzzle ~ Covering a Chessboard With Dominoes

Crystal Clear Maths
Crystal Clear Maths
10,378
0
Published 2014-10-31
Take a chessboard and remove two squares from opposite corners. There are now 62 squares remaining. If you take 31 dominoes that each cover two squares, is it possible to arrange them so they completely cover the 62 squares?

If you are like most people, you will get or make a board or draw a diagram and try it out for yourself. After a few attempts, you may begin to believe this is impossible. But ... is it impossible? Is there a clever solution that you overlooked, or is it possible to prove that no solution is possible?

Mathematicians are able to analyse problems like this using a concept of parity ... in this case, the black and white squares of a chessboard. Watch this video and learn how this very clever insight is used to prove whether the problem is solvable, or not!

I hope you enjoy!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For more information about mathematics or how to study, visit my website, Crystal Clear Mathematics at www.crystalclearmaths.com/

If you wish to be kept up to date with what I am producing on the website (ad free, spam free, cost free mathematics and study materials), please add your name to the mailing list there.

Download my FREE 32 page PDF "How to Study" booklet at crystalclearmaths.com/wp-content/uploads/2015/12/H….


Best wishes for your study and your mathematics!
All Comments (12)