You face a room of very hungry people.  A large pizza arrives and you are handed a knife and asked to cut the pizza into as many pieces as possible using just three straight cuts.  Because the pizza is very hot you cannot move any of the pieces (e.g. stacking them on top of one another and then cutting).  What is the maximum number of pieces that you can create using just three straight cuts?

As ever, please do NOT post your answers, but do feel free to say if you think you have solved it and how long it took.  Solution on Monday.

 

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64 comments

    1. P(n) equation not the biggest answer…. possible to get more than that as pizza is a 3-dimensional object.

    2. @Waddett I think in this case we can assume that a pizza is a 2D object. If no, i choose the upper part. 😉

    1. Ok you win!

      But even when sticking to Euclidian geometry the answer does depend an the dimensionality.

  1. i have an euclidian solution but it seems quite unfair to some of the Pizza eaters. less than one minute…
    However i suppose it is not intended to place the whole pizza on a ape saddle shaped disch before cutting…

  2. I think I have the answer, but I’m worried I might have overlooked some sneaky way of getting more.

    At least my way ends up with pieces of equal area, and equal amounts of base and topping in each piece, which might be important in a room of very hungry people!

  3. It’s not clear whether the pizza can be treated as a 3D object like a cake or just a 2D one. The answers are different; but then, a 2D pizza wouldn’t be very filling however big the slices were.

  4. The number of the solution also depends on the question if i habe to use always the same knive and if it might habe a curved / bend blade…

  5. Well, I have one solution that results in three different sizes of piece (multiple big, multiple small, and possibly one medium)… so I suppose if the party comprises both adults and children no-one will mind.

    Otherwise I’d suggest either cutting more slices or asking if anyone’s got the phone number to the nearest pizza delivery service to order additional ones… 🙂

  6. 1 pizza for a room full of hungry people? Then cutting it into as many (i.e. small) pieces as possible? The answer can only involve personal injury!

  7. If there isn’t a trick then it’s easy, if it does involve curved spacetime or multiverses then I’m stuck.
    and
    I’ve already had a bite out of it so that skews things too.

  8. The original puzzle took place at a Pizza Hut in Croydon where everyone perished from hunger before it arrived. True story.

  9. About two seconds to get an obvious answer but then as it’s so obvious it’s bound to be wrong. Will ponder on ot some more

    1. you are right if pizza is flat. but if you consider its thickness, i can cut it higher than 7

  10. As long as I got the knife, I’m in charge.
    I’ll tie the pizza to a chair and dance around it singing “Stuck In The Middle With You”.

  11. Two one answers, one if we assume the pizza is a 2D object, one for 3D. There’s a multiple set of answers based on if the pizza is deformed before we cut it.

  12. I have an answer, but I doubt it’s correct.

    Just some thoughts, though:
    Even allowing for the curvature of the earth, if the line is straight it’ll finish where it started, and you can’t move the pizza because it’s too hot, so it’ll still be one cut.

    I think cheating by slicing the pizza in two thin pizza halves (effectively making a pizza sandwich) is wrong; some people wont get any topping, which is clearly unacceptable 😉

    You could of course cut it into an almost infinite number pieces as you want using just three straight cuts, provided that they’re followed by as many curved cuts as you like :p

    (This is me cheating, and I hope it doesn’t constitute an answer)

  13. There’s only one solution if we treat the pizza as a 2D object, another one if we can treat it as a 3D object (which seems to defy the “too hot to stack” instruction), and the solutions if we can deform it as a 2D object in 3D space (which seem even less reasonable) are probably limited but beyond my math/geometry skills.

    A few seconds to think of the 2D solution and straightforward 3D solution, a few minutes of musing to decide the more exotic geometric solution were too much work.

    –Dave

  14. Put Pizza down on record player and can get a whole lot of pieces with straight lines. Many angry guests who I assume will not fall for the is not vinyl, the pizza is just a bit burnt line however…

  15. If my answer is correct, then it’s ridiculously simple. But I suspect there’ll be something much more impressive revealed.

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