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        riddles >> easy >> Easy: 8 way circle slice
        
(Message started by: cnmne on Jul 30^th, 2002, 2:18pm)

Title: Easy: 8 way circle slice
Post by cnmne on Jul 30^th, 2002, 2:18pm

I do not see how you can divide a plane into more than seven sections, let alone a circle into eight sections of equal area or equal shape.

I do not think this can be done in two dimensions.

If you give the circle depth then it is the easy cake problem.
If you draw the circle on paper and fold the paper, then it can be done in three folds.

Is there an answer to this problem as stated?

Title: Re: Easy: 8 way circle slice
Post by william wu on Jul 30^th, 2002, 3:55pm

Yes, there is a solution ... I cut out a circle from a campus cafeteria napkin yesterday and did it :)

There are two solutions I know of to the 8-way cake slice problem, and one of these solutions can also solve the 8-way circle slice problem.

Note that the 3D solution you are thinking of for the 8-way cake slice problem does not require you to manipulate the cake in any way aside from simply slicing it.

Rearrange stuff to get more mileage per slice. Good luck!

Title: Re: Easy: 8 way circle slice
Post by Blender on Jul 31^st, 2002, 1:35pm

Presumably the riddle would have said "Using this knife, slice this piece of round paper into 8 equal sized pieces using 3 straight cuts."

But as far as I know, a circle is 2 dimensional which implies that it's a geometry problem that you should be able to solve on a blackboard with a piece of chalk. If this is the case, your paper napkin solution doesn't work.

I can only figure out how to get 7.

What is the real answer?

Title: Re: Easy: 8 way circle slice
Post by ScottP on Jul 31^st, 2002, 11:17pm

I'm with cnmne and Blender - looks like the only way to do this if it is down using cuts rather than lines.... and then manipulating the sections in 3D space. Willing to be proved wrong though.

Title: Re: Easy: 8 way circle slice
Post by william wu on Jul 31^st, 2002, 11:20pm

You guys are absolutely right. The problem statement is misleading. I will rephrase it later so that it is clear you are allowed to do post-cut manipulation in 3d space.

No, I changed my mind. I'm just going to add a footnote to the 8-way cake slice problem: Find 2 solutions.

Thanks guys :)

Title: Re: Easy: 8 way circle slice
Post by Oski Bear on Aug 5^th, 2002, 5:47pm

but it's not a 2D circle. it's a CAKE, which has 3 dimensions. so if the cake is in front of you on a table, do this:

1st cut: divide the cake in half
2nd cut: forms a + sign with first cut. the cake is now in quarter slices
3rd cut: slice "horizontally" to divide the cake into 2 circular planes (each being half the height of the original cake). each plane is already divided into four pieces, so now you have eight.

Go Bears

Title: Re: Easy: 8 way circle slice
Post by william wu on Aug 5^th, 2002, 5:50pm

Hiya Oski. To explain the title of this thread, there used to be a riddle called 8 way circle slice, which asked how to divide a 2D circle into 8 equal pieces using 3 slices. Then I deleted it from the archive, and just modified the cake problem so that it now asks for 2 solutions. The solution that you mentioned would only work for a 3D cake, but not a 2D circle of paper.

Go Bears :)

Title: Re: Easy: 8 way circle slice
Post by ckb on Aug 6^th, 2002, 4:52pm

Here's my take on the cake slicing:

1. Slice down the middle (2 pcs)
2. Slice down the middle the other way (4 pcs)
3. Take the quarter pcs and line them up in a row like this:
>>>>
Then slice through all of them.

That gives you 8 equal sized pieces AND each piece is equally frosted (assuming that the cake is frosted on all sides and on the top)
If you slice horizontally through the middle, parallel to the table, then 4 people get no frosting toppings.

ckb

Title: Re: Easy: 8 way circle slice
Post by william wu on Aug 6^th, 2002, 7:31pm

interesting, i never even thought about the frosting. i guess the transverse plane slice method is suboptimal. you get an A+.

Title: Re: Easy: 8 way circle slice
Post by Kujo on Aug 9^th, 2002, 7:15am

The problem does not state the cake is frosted. Furthermore, if it was frosted, the frosting is not the cake itself. The pieces of the cake are still equal.

Title: Re: Easy: 8 way circle slice
Post by Luke on Feb 8^th, 2003, 10:07am

SO what is the answer? I thought of some ways thinking this was a real 3D cake. Can't figure it out if it was just a 2D circle.

Title: Re: Easy: 8 way circle slice
Post by Speaker on Feb 10^th, 2003, 12:45am

I didn't have a cafeteria napkin, so I just used a post it, and aside from one sticky edge, had no problem.

I just folded the circle up and with one slice created 8 equal pieces. Is that it? It seems pretty easy. I just folded it in half, and then in quarters, and then folded the edges back to make a fan sort of paradigm, and then sliced it down the middle.

Title: Re: Easy: 8 way circle slice
Post by bashar haddad on May 26^th, 2003, 12:12am

First step: cut down the middle.
Second step: cut down perpenticular to the first cut.
Third step: line up the 4 slices you already cut like this:
<| <| <| <|
and cut down the middle of them all, you get 8 slices all with frosting...= ]

Title: Re: Easy: 8 way circle slice
Post by grimbal on May 18^th, 2004, 6:13am

on 08/06/02 at 19:31:43, william wu wrote:

interesting, i never even thought about the frosting. i guess the transverse plane slice method is suboptimal. you get an A+.

Just assume there is frosting on the top and the bottom. ;D

Anyway, with a napkin, you could just fold it 3 times to get a 1/8th of a dîsk and cut it along the median. Unfold and ... voilà! It even works with a cake ... a pancake.