The Pizza PI Day Paradox

Logic Level 2

Divide a Pizza evenly among 3 people, but all you can do is cut the pizza or any piece of a pizza in half. Hint, if you can't get started try dividing the pizza between 2 people and then 4 people.

Cut the pizza in half and then cut each slice in half. Give each of the 3 people a slice and give the remaining slice to the dog. Cut the pizza in half and then cut the 2 slices in half. Give each person 1 of the four slices with 1 remaining. Cut the remaining slice in half and then the two slices in half. Give each of the 3 people a slice with 1 slice remaining. Continue on Cut the pizza in half an don't give one person a any. Cut the pizza in half and then cut each slice in half. Give each of the 3 people a slice and throw away the remaining slice.

M Jr by M JR , 65, USA

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1 solution

If the pizza is cut in four equal slices and each is given one slice, then each gets 1 4 t h \dfrac{1}{4}^{th} of the pizza. If the remaining 1 4 t h \dfrac{1}{4}^{th} of the pizza is again cut in four slices and each is given one slice, then each gets 1 16 t h \dfrac{1}{16}^{th} of the pizza. If this process be continued indefinitely, then each gets ( 1 4 + 1 16 + . . . ) t h (\dfrac{1}{4}+\dfrac{1}{16}+...)^{th} or ( 1 4 1 − 1 4 ) t h (\dfrac{\dfrac{1}{4}}{1-\dfrac{1}{4}})^{th} or ( 1 3 ) r d \boxed {(\dfrac{1}{3})^{rd}} of the pizza, so that the pizza is evenly distributed among them.

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For such a simple problem it touches on a surprising number of mathematical concepts and problem solving strategies. The primary goal of this problem is to explain to young people the concept of division without much math. By using a common everyday occurrence, splitting a pizza, it helps them to understand the need for division.

The hint is an example of using simplifying assumptions in order to get started on any problem.

Cutting things in half is an example of bisection, something they will see later in geometry.

Cutting things in half is an example of binary numbers, something they will see later in computing.

Since the number of slices and people don't divide evenly it introduces remainders.

Since the number of slices and people will never divide evenly it introduces relative primes.

Since the numbers are relative primes it introduces iteration.

Iteration introduces series.

Series introduces asymptotes.

More can be learned by changing the number of people. 5, 7 & 9 are interesting but so are 6 & 8.

M JR - 1 year, 4 months ago

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