perplexus.info :: Shapes : Chocolate!

Chocolate! (Posted on 2002-06-12)

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.

Submitted by TomM

Rating: 3.6000 (10 votes)

Solution: (Hide)

The answer is 31.
In fact, every allowed way of the breaking the chocolate bar into single squares will take 31 breaks. This is because each break you make increases the number of pieces you have by exactly 1. For example, you start with 1 piece and after your first break you have 2 pieces no matter what break you choose to make.
Similarly, after two breaks, you have three pieces, and after three breaks, four pieces. Since you end with 32 pieces (namely the 32 single squares in the bar), you must have made exactly 31 breaks.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
answer	K Sengupta	2007-05-15 04:25:54
can't i stack them? =)	Amon	2005-05-05 00:46:46
re: bob is right (where did the other row go?)	Charlie	2003-04-11 10:16:31
bob is right	Jon	2003-04-11 08:36:23
re: About the hints	Nick Reed	2002-06-12 23:07:36
Solution...	Half-Mad	2002-06-12 20:14:18
About the hints	TomM	2002-06-12 18:36:27
My solution	bob	2002-06-12 10:35:12
re2: Also errr	Nick Reed	2002-06-12 08:21:52
re: Also errr	levik	2002-06-12 06:35:32
Also errr	Nick Reed	2002-06-12 06:18:54
err..	Cheradenine	2002-06-12 05:52:11
'Helpful' Hints	TomM	2002-06-12 04:25:01

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