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Pizza

Twelve friends want to share a pizza. One of the friends is very fussy and will not eat the centre of the pizza.
Is it possible to split a (circular) pizza into twelve identical pieces such that there is at least one piece which does not touch the centre?

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If you enjoyed this puzzle, check out Sunday Afternoon Maths LXI,
puzzles about lines, or a random puzzle.
© Matthew Scroggs 2017