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?
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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