Breaking up can be sweet solution

May 2004

Breaking up can be sweet...


I can't wait for Easter to get here, so I have bought myself a block of chocolate to tide me over. It is a normal rectangular-shaped block with 5 rows, and 4 pieces of chocolate to a row, making 20 pieces of chocolate ready for the eating. I want to eat all of it right now, but I want to savour each piece.

What is the least number of clean snaps necessary to break the block of chocolate into the 20 individual pieces?

What about for a block with n rows of m pieces?

The solution

The solution to this puzzle is really pretty simple - but, as usual with maths, only if you think about it the right way!

Each snap creates exactly one extra piece, therefore to break a bar with K squares of chocolate into all its constituent pieces will require K-1 snaps. So if the block has n rows of m pieces, it will take nm-1 breaks.

And that's all there is to it!

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Why is it not 17? If you half each time. Ie. first cut creates 2x4 and 3x4. second and third creates 2 blocks of 2x2 and 2 blocks of 2x3. The first 2 2x2 require 3cuts each the second 2x3 require 4 cuts each. 3+3+3+4+4=17

Doesn't each 2x3 require 5 cuts?