[Guest]

I'm having deep-dish pizza tonight (Pizzeria Uno's ... mmmm), and figured I'd try to think of a puzzle about it.

There's a classic problem about a mom and 2 kids, and how to cut some food (let's call it pizza for this riddle) into two pieces so that both kids are happy they got exactly half. I'm sure that problem's on here if you want to search, read it spelled out clearer, but if you want the basic solution, here it is.

Have one kid cut it in half, and have the other kid choose which piece they want.

Anyway, my thoughts turned to having 3 kids, and I was stumped at a fair way to do this. For one, dividing a region in 3 equal parts versus 2 equal parts is much tougher, ranging to impossible with a circle and pizza. Also, the solution in the original problem (above in the spoiler) doesn't easily apply here.

I've come up with a mediocre, complicated solution, and am interested in what everyone else can come up with. There are not wrong answers here, although there are better answers than others.

A couple of rules:

1) All 3 kids should end up with the same amount of pizza, or a situation that they feel is fair (like the original problem).

2) The entire pizza must be consumed by the 3 kids. Otherwise, just doing a version with cutting it into 4 pieces and saving 1 for leftovers could work somehow.

[Guest]

Have kid 1 cut what he estimates is 1/3 from the pizza. Have kid 2 split the 2/3 piece in 1/2. Have kid 3 pick any of the 3 pieces and kid 2 pick one of the 2 pieces he cut, leaving the last piece for the first kid.

Edited April 12, 2008 by imtcb

[bonanova]

First child cuts a piece from the pie.

Next child may make the piece smaller or pass.

This continues until everyone passes.

Last child to touch the piece gets it.

Continue the process until each child has a piece.

The nice thing about this approach is that it works

for any number of children, not just three.

[Guest]

hve one kid to cut it and the other chooses which piece he wants

i think i've seen this one before

have the first child to cut a piece then have the next child to either make the same piece smaller or not do anything keep going until every child has passed his turn to cut the piece. Continue with this for the whole pizza

Edited April 13, 2008 by andreay

[Guest]

The problem with bonanova and andreay's solutions is that if kid 1 wants to give kid 2 a bigger piece, kid(s) 3(+) can do nothing about it. In my example there can be no favorites without cutting yourself the shortest in the process.

[Guest]

The problem with bonanova and andreay's solutions is that if kid 1 wants to give kid 2 a bigger piece, kid(s) 3(+) can do nothing about it. In my example there can be no favorites without cutting yourself the shortest in the process.

Thats the whole idea imtcb. Assuming the kids are all wanting the largest portion possible then none of them would give themselves the smallest piece to give someone else a larger piece

[Guest]

Thats the whole idea imtcb. Assuming the kids are all wanting the largest portion possible then none of them would give themselves the smallest piece to give someone else a larger piece

The OP requires that ALL kids find the division fair. If the 3rd kid has no say in the way the pieces are cut or distributed he could definately say it isn't fair. What if kid 1 slices the pizza in half for whatever reason, and kid 2 takes an entire 1/2 of it! My way, there is no way that any of the 3 could be upset because they either cut or picked before any pizza is eaten.

[Guest]

Like the answers so far. But I'm missing something from a few people's answers.

When people are saying about making a piece smaller, does that imply you're making another piece bigger? Or is that little bit that's taken away go into a scraps pile?

Because if it's the second one, it doesn't satisfy one of my conditions: that the whole pizza gets eaten by the 3 kids. I don't have a problem with the little bit lost by cutting, but I think any intentional wasting of pizza (like making a piece smaller to make it even and not doing anything with that little bit) violates the condition.

Or maybe I'm just not understanding those solutions...

[Guest]

Just blend it and pour/serve using teaspoon and a nose drop for the last bits (not in the nose though)

[Guest]

Just blend it and pour/serve using teaspoon and a nose drop for the last bits (not in the nose though)

Now that's what I call lateral thinking!

Personally, I've never liked the whole business of letting one kid cut and another choose to achieve fairness. If you were a kid, which role would you choose? Cutter or chooser? Chooser, obviously, because it's not easy to eyeball a cut to achieve fairness, no matter how hard you try. In all of the suggested solutions (except for the one by LIS), somebody will inevitable get the shaft, no matter how selfless the kids are. So ...

... just use math. First use two pieces of string to find the center (making an X from opposite sides will get you really close), then use the string to get the circumference, divide the length by the number of kids, cut off a length of string to the arc of a single-piece, and use it to mark where to cut. If you do it yourself, it will probably be more accurate and faster than letting the kids do it. If you're concerned about the slight differences, mark each piece with a number and have them draw from a hat.

[Guest]

Now that's what I call lateral thinking!

Personally, I've never liked the whole business of letting one kid cut and another choose to achieve fairness. If you were a kid, which role would you choose? Cutter or chooser? Chooser, obviously, because it's not easy to eyeball a cut to achieve fairness, no matter how hard you try. In all of the suggested solutions (except for the one by LIS), somebody will inevitable get the shaft, no matter how selfless the kids are. So ...

_ at some point that need to practice what we teach, let them have a go, supervise (patiently if possible)

Old Benny Hill sketch - Polite man offers out plate with two cakes to a friend, the friend chooses the larger one. Polite man says - "If I had first choice I would have chosen the smaller one". Friend replies - "But you've got the smaller one".