I can't take credit for this. It was submitted to a quiz page on the CBC's (Canadian Broadcasting Co) website by Professor Maria Klawe of the Computer Science department at the University of British Columbia. But I thought our group would enjoy it.

Remember when a bar of plain milk chocolate was scored to allow you to break it evenly into smaller pieces?

What is the smallest number of breaks needed to divide a 4 by 8 chocolate bar into single squares, where each break splits any one of the pieces along an original horizontal or vertical line of the bar? Your answer should explain why your number is the smallest possible.

I can't give away the answer, but I can give out some hints. Not all of them will be as helpful as they seem.

Consider the scratched checkerboard problem. What is the relationship of the breaks to the original scores along which you made the breaks.

If you make all the horizontal breaks first, you will have more individual vertical breaks to make and vice-versa

What exactly do you get each time you make a break?

Posted by TomM on 2002-06-12 04:25:01