21 Aug 2013

8 Slices of Pizza: Mathematical Puzzle

Half a pizza is never enough – especially if, like Brenda, you actually had less than half. So, Alice and Brenda were back in the kitchen on a mission, opening all the remaining pizza boxes.

“Found one!” beamed Brenda. “This time, let me cut it.” Alice looked sceptical, but thought it was fair enough. Brenda first cuts it in exactly the same way as Alice did, with two perpendicular cuts passing through a point that was not the centre of the circular pizza but lay within it. Before Alice could utter a word, Brenda cut her short, “But now I’m going to make two more cuts.”

Brenda’s two cuts went through the same common point and bisected the right-angles. There were now 8 slices of pizza, as shown in the diagram. “Now, let’s number each slice in sequence from 1 to 8. Would you like the even-numbered slices or the odd-numbered ones?” Alice looked at the pizza and thought... and thought... “It’ll get cold!” said Brenda impatiently. “Cold-er!” was Alice’s laconic reply.

So which slices should Alice take? To make the diagram easier to look at, the even-numbered slices are in red and the odd-numbered slices in white.

Red or White?

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