Tomorrow I am speaking at the Anomalistic Research Unit in London. Hope you can make it!

On Friday I posted this puzzle…..Five people order a square pizza. The first person dives in an eats a quarter of the pizza. The other four people have to divide the remaining three-fourths into four equal and identically shaped slices. The cuts must be straight. How must they cut the remaining pizza in order to produce four identical slices?

If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.

OK, here is one answer…..

Did you solve it? Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for theKindle (UK here and USA here) and on the iBookstore (UK here in the USAhere). You can try 101 of the puzzles for free here.

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This one was easy, but then I have seen it before. I wonder how long it would take for people who have never seen it. I also wonder how many people mistakenly thought the andwe would be triangle shapes (not possible as the sizes wouldn’t match).

*Answer – not andwe. IPhone spellchecker fails all too often.

Yes got it.

But as I said, I hope people are not going to complain about not having the same size of crust. One of them does not get any crust at all.

That would willingly be me. I hate crust…

Actually, because of the shape of the pizza, they all get two sides of crust or more!

I volunteer for the crustless piece. Who wants crust anyway? That’s like dry bread. It’s what they used to serve prisoners.

@AMWhy:

Read again, the pizza was initially square. So the middle piece has no crust at all.

That’s indeed the answer I got.

AMWhy, you forget that the original pizza was square. So, the middle piece gets no side crust.

I did it by continuing each of those four cuts from crust to crust. Everyone gets three pieces and the same amount of crust.

We cut it into three squares, then quartered those so each person gets a quarter-sized wedge from eachof the three remaining sqaures. Not as elegant as the solution but it still works.

Doesn’t quit fit however, as the puzzle asks for just 4 slices / pieces.

I went for the most direct solution… The first quarter slice is made by slicing an edge off the pizza, 25% of the width. A long thin slice, I hope the anchovies align.

The remaining 75% is now also sliced into 4 equal strips. Admittedly 3 slices have only narrow strips of crust top and bottom and one slice has crust on 3 sides, but single cuts, and easy to estimate as halves of halves of a linear dimension? Pretty straightforward.

Soo…you have five pieces which aren’t the same size or shape, cut from a pizza which was a different shape to the one pictured. Which puzzle were you trying to solve?

I did the same as you. The original on Friday didn’t have a picture when I read it. Maybe it was added later or maybe my phone failed to display it. But with that extra latitude I decided also that if the first quarter removed was a single strip off the side, that would leave multiple trivial solutions to dividing the remainder into four.

I did struggle on assuming that the initial quarter had been removed as pictured or even as a triangle but didn’t manage to come up with the solution.

Quiote right Alex – our solution fits, but there are 12 slices to be divvied up rather than 4. Shame, we were so pleased with ourselves.

Neat!

I hadn’t seen it before and found it quite easy. I thought of the remaining pizza as 3 squares, which meant that between four people each would have 3/4 of a square. The first shape I then tried was a small version of the shape of the pizza, and bob’s your uncle, there it was.

Chop the 3 remaining quarters into squares. Chop all 3 squares down both diagonals. This will give you 12 equal pieces. Divide these by 4 so each remaining person gets 3 equal sized pieces

I don’t think anyone’s mentioned making three cuts parallel to the plane on which the pizza is resting. Would be a bit tricky and a bit toppingless for the bottom three though.

I want the top part!

What a sacrifice! Are you always so altruistic? LOL

First cut from top right corner to bottom left corner. Second cut from bottom right corner to the bottom right corner of the missing piece. Result: 4 equal triangle pieces with 2 cuts. Send the bill to the freeloader that took the first slice.

They’re not equal slices, 2 slices would be smaller than the other 2

Hmmm, peanuts! :-)

I did solve it :D

The puzzle stated ‘The cuts must be straight.’. This solution has cuts with angles in them. This is not a valid solution.

Agreed. A line kinked at a 90 degree angle is not a line I would call “straight”. Moreover, it violates the spirit of the puzzle: a round pizza cutter would not easily make those cuts!

Indeed, following the spirit rather than the letter of the rules, it would actually be easier to make a curved cut than one with sharp angles!

‘a cut with a 90 degree angle in it’..? Surely that’s two straight cuts

Exactly. I knew the solution presented here but wasn’t allowed to go there because of the line “The cuts must be straight”.

I LLLLike pizza

how can they be identically shaped if there edges are not the same? three have some edges of crust, the forth one doesnot.

How do you know the pieces are the same size, unless you have a ruler and a straight rule? And if you need tools like that, then this is nothing but one arbitrary solution – just one of an infinite number of possible solutions is it not?

Neat answer, but I do not see how you could do it with an unmarked straight edge (a knife) alone. You would need a ruler to find the center of the sides of the squares. You could find the centers by finding where the diagonals cross, but unless you marked up a scale drawing with a pencil before you cut the pizza, you would have to make additional cuts in the pizza and end up with a number of triangles. I came up with a solution that gives me three pieces that each look like squares with a triangle cut out of one quadrant. Then the three cut-out triangles can be rearranged to form a fourth square with an empty triangle in its fourth quadrant just like the other three. There was nothing in the problem statement that precludes this kind of rearrangement and it can all be done with a knife only.

well, i’m kind of pleased. It took me about 3 minutes, and i’d never seen it before. But I think I’d have had it sooner if I hadn’t assumed at first that “straight cuts’ meant something you could do with a pizza cutter. Those inside corners wouldn’t work well for that!

I figured I would cut 3/4ths off of each “leg” and cut the remaining stumpy backwards “L” diagonally in half (from the inside corner to the outside corner).

This would require only three (straight) cuts but they wouldn’t be identical slices. However, everyone would get the same area of pizza (if my maths are correct) and also get some crust.

Can anyone prove that is the only solution? Hmm. I can’t even prove the 3 houses and gas, water and electricity puzzle is impossible.

Nice

I think the best example for this problem is to apply it to a lot ,the quarter donated to church and the remaining 3/4 will be divided to four heirs. What do you think..