Brain Teasers
Pizza Pieces
What is the largest number of pieces you can form with n straight cuts of a pizza?
The pieces do not need to be of equal size.
The pieces do not need to be of equal size.
Answer
The answer is n*(n+1)/2 + 1.With every cut you should cut through every previous cut. As long as you keep doing this you will always be able to do so again with your next cut. The number of additional pieces formed on cut x will always be x. The sum of all integers from 1 to n is n*(n+1)/2. So the sum of additional pieces cut will be n*(n+1)/2.
Finally add 1 because we start with 1 piece: n*(n+1)/2 + 1.
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Comments
numbers and letters everywhere
huh?
So for 3 cuts, there must be 7 slices, right?
Slices = 3((3+1)/2) + 1 = 7.
But what if after I cut it twice, (leaving me with 4 slices), I cut it in the middle in such a way that I now have 4 slices with toppings, and another 4 slices with only the crust! That gives me 8 slices in all, not just 7!
Slices = 3((3+1)/2) + 1 = 7.
But what if after I cut it twice, (leaving me with 4 slices), I cut it in the middle in such a way that I now have 4 slices with toppings, and another 4 slices with only the crust! That gives me 8 slices in all, not just 7!
Please don't cut it into 8 slices - I couldn't eat that many pieces!
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