Suppose you have a pizza being cut vertically with one straight cut, you'll be left with two pieces. The ratio of number of pieces to cuts in such an instance will be 2 (a whole number, i.e. no remainder).

If you cut a pizza using two straight vertical cuts, you'll have four pieces left (pieces-to-cut ratio = 2, also a whole number).

Cutting the pizza thrice, the maximum pieces possible is seven (pieces/cuts = 7/3 = 2.3333..., i.e. there is a remainder of 1).

See attached image.

Questions ...

(1) What is the maximum number of pieces that one would get by cutting the pizza 500 times using only straight vertical lines (no horizontal cuts allowed)?

(2) How many cuts should one make to get a maximum of at least 5 million pieces?

(3) The minimum piece-to-cut ratio with no remainder is exactly 2 as indicate above. What would be the next higher number of cuts, such that the number of resulting pieces divided by the number of cuts has no remainder?

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## rocdocmac

Suppose you have a pizza being cut vertically with

onestraight cut, you'll be left withtwopieces. The ratio of number of pieces to cuts in such an instance will be 2 (a whole number, i.e. no remainder).If you cut a pizza using

twostraight vertical cuts, you'll havefourpieces left (pieces-to-cut ratio = 2, also a whole number).Cutting the pizza

thrice, the maximum pieces possible is seven (pieces/cuts = 7/3 = 2.3333..., i.e. there is aremainderof 1).See attached image.

Questions ...

(1) What is the

that one would get by cutting the pizzamaximum number of pieces500times using only straight vertical lines (nohorizontal cuts allowed)?(2)

cuts should one make to get a maximum of at leastHow many5 millionpieces?(3) The minimum piece-to-cut ratio with no remainder is exactly 2 as indicate above. What would be the

, such that the number of resulting pieces divided by the number of cuts has no remainder?next higher number of cuts## Link to comment

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