# Cutting a pizza into largest number of pieces

…with 4 straight cuts .

I was reading “Classic Brainteasers” by Martin Gardner (Orient Paperbacks edition ).

He gives the solution as 11 with illustrative figure.( The formula applicable is 0.5 xsquared +0.5 x +1, with x being number of cuts).

Now if the 4th cut is made horrizontally through the centre of pizza ,one can get 14 pieces ( double of 7 pieces ).

Only condition specified is 4 straight cuts, not size of pieces.

What am I missing ?

He’s assuming, without explicitly stating, that the “pizza cutting” represents a 2D problem. Else the brainteaser would be “watermelon cutting” or some such.

If you’re suggesting a horizontal cut will produce twice as many slices of pizza, please review your logic. The question specifically asks for the largest number of pieces of pizza. Your solution would result in zero.

Naw, there’d still be 7 slices of pizza and seven slices of bread. And there are covered pizzas where 14 would actually be the correct answer.

(Of course, I’m assuming the definition that a pizza is "A baked pie consisting of a shallow bread crust covered with toppings such as seasoned tomato sauce, cheese, sausage, or olives.)

Seriously!?
Honestly, why do some people insist on inventing exceptions and modifying the question and/or the definitions of the terms to suit their own ridiculous answers? :dubious:

The question asks for pizza, as **zut **said…

If you want to start breaking the rules of a basic 2-D puzzle I’m sure there are even more ways to do it than just a horizontal cut.
How about folding the the pizza in half a few times then making the cuts?

Yes ! It is meant to be a 2D puzzle.
I rechecked that puzzle .** It is apple pie and not pizza.**:smack:

As if that makes a difference?

No it won’t

I don’t know. Is it with ice cream or without? Also, are we really talking ‘slices’ or did it say ‘pieces’? Some apple pie crusts are really flaky.

You can’t fold an apple pie.

Then how do you fit it in your mouth?

That’s what she said.

Open it really wide

That’s what he said.

I think the OP is worded in a way that supposes we are familiar with this puzzle already, which I’m not. Are these pieces meant to be congruent pieces? Non-congruent but equal in volume? Or just “get as many fragments of any size you can” with 8 straight cuts? And what does “straight cut” mean – through center (diameter), edge to edge (chord of the circle), one point of the cut must touch the edge of the pie but not both, or just “no wiggles”?

Because if the intuitive meaning of “cut this pie” (meaning, into equal and identical pieces with straight line cuts that go from one edge to the other) is in play I don’t see how it can’t be 8 and only 8.

OK if it’s just “any number of fragments” I just drew on on a piece of paper with four lines edge-to-edge (chords) resulting in 11 fragments. Are you saying even more is possible?

you have to make as many pieces as possible without regard to size or shape of the pieces. All “straight cuts” means is a chord (why would you stop anywhere but to the edge, it will never result in more pieces than going to the edge) with “no wiggles”.
And to the OP, like another said, the point of the puzzle is that it’s 2D and maximizing the number of intersections; it’s just more interesting to talk about a pizza or a pie than a circle and let the 2D part be an implied restriction. Besides, one could argue that it stops being a piece of pizza if you make a horrizontal cut because the bottom pieces would just be baked bread, not pizza. Also, if it were a 3D puzzle, I think you could get more than 14 pieces if you allowed diagonal cuts, but I can’t be sure since I can’t easily draw it out and count pieces.

Well if the solution is given as “11” then I guess I’ve got it, or some variant of it. But it intrigues me to think of how I might PROVE that this is the largest number. Hmmmm.

Visually, I drew a circle, slashed three lines in it like an A so it kind of looks like the Anarchy logo, giving me 7 segments. I then laid a fourth line diagonally across, like taking the crossbar of the A and rotating it 30 degrees around the middle of the line. Then I counted the segments between the lines and it comes out to 11.

Yes, it’s actually very difficult to slice an apple pie so that you end up with a piece of pizza.