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Subject: "Cutting a pie in 8 pieces in 3 movements"     Previous Topic | Next Topic
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Conferences The CTK Exchange This and that Topic #643
Reading Topic #643
Cutting a Pie
guest
Oct-01-05, 10:13 PM (EST)
 
"Cutting a pie in 8 pieces in 3 movements"
 
   https://www.cut-the-knot.org/do_you_know/cake.shtml

How is that possible when the formula for this is 1/2(n^2 + n + 2)?

The max number of pieces is 7, isnt it?


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alexbadmin
Charter Member
2209 posts
Oct-01-05, 10:32 PM (EST)
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1. "RE: Cutting a pie in 8 pieces in 3 movements"
In response to message #0
 
   >https://www.cut-the-knot.org/do_you_know/cake.shtml
>
>How is that possible

Well, this is what this page is about. Have not you read it?

The formula you cite relates to a sequence of vertical cuts. The 3 cuts solution does not fit into this framework because one of the cuts is horizontal.


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guest
guest
Oct-03-05, 06:23 AM (EST)
 
2. "RE: Cutting a pie in 8 pieces in 3 movements"
In response to message #1
 
   Dont know what I'm doing wrong but the most I can get is 7.

3 lines like this?

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Have no idea why im not getting this, it'seems simple enough.


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alexbadmin
Charter Member
2209 posts
Oct-03-05, 06:45 AM (EST)
Click to EMail alexb Click to send private message to alexb Click to view user profileClick to add this user to your buddy list  
3. "RE: Cutting a pie in 8 pieces in 3 movements"
In response to message #2
 
   >Have no idea why im not getting this, it'seems simple
>enough.

Right. If you cut 4 of something (sausages, say) put side by side so that you are able to cut all 4 with one cut, you get 8 pieces.

Unquestionably, you can cut the pie into 4 pieces with 2 cuts. Imagine now the pie put on a side, so that all 4 pieces become exposed to a vertical cut. Do it.

The 8 pieces you obtain are not exactly what one would expect: 4 come from the bottom of the pie, 4 from the top. The latter carry all the toppings and, in all likelihood, are more desirable. The former may be less hazardous to one's health, though.


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Pete
guest
Mar-25-08, 03:43 PM (EST)
 
4. "RE: Cutting a pie in 8 pieces in 3 movements"
In response to message #0
 
   Someone asked me this and the best answer I got was cut the pie in half, stack the halves on top of each other, cut that in half, and then stack the quarters on top of each other, then cut that in half. Thus you get 8 pieces with 3 cuts. Though I'm not sure if stacking the pieces is exactly legal. Since I never found out the answer to the riddle.

Pete


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alexbadmin
Charter Member
2209 posts
Mar-25-08, 03:48 PM (EST)
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5. "RE: Cutting a pie in 8 pieces in 3 movements"
In response to message #4
 
   This thread is exactly about this problem. Just read it. Ot have a look at

https://www.cut-the-knot.org/do_you_know/cake.shtml


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