Wednesday, February 10, 2010

What is the number of breaks needed to split the bar into 10 smaller 1x1 squares?

Consider a chocolate bar consisting of squares arranged in a 2x5 rectangular pattern. What is the number of breaks needed to split the bar into 10 smaller 1x1 squares, if one must always break along the lines between the squares and if stacking and breaking isn't allowed.What is the number of breaks needed to split the bar into 10 smaller 1x1 squares?
Nine breaks.





However you do it, it is nine.





If you break it long ways first and then break each strip into five that is one break then two lots of four breaks.





Or if you break it four times and then break each double in half that is one plus eight breaks is nine again.What is the number of breaks needed to split the bar into 10 smaller 1x1 squares?
5 breaks.

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