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Using a knife to make four straight-line cuts,

how many pieces can a single pancake be divided into?

Generalize for N cuts.

I think 11 pieces... But not sure how to generalize.

Edited by Noct
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You can get more than that. Can you think of a way how?

Sure we can(10), but they wont be equal sizes and we will not be able to genralise it to N cuts.

Circle -> 2 horizontal straight lines one on top and one at the bottom. Now draw and X thus we have 4 straight lines and 10 pieces. But they will not be equal and will not be sectors, they will be different shapes.

Let me know if there is a way to get more than 10 with 4 straight line cuts.

post-5551-1206250444_thumbgif

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Sure we can(10), but they wont be equal sizes and we will not be able to genralise it to N cuts.

Circle -> 2 horizontal straight lines one on top and one at the bottom.

Now draw and X thus we have 4 straight lines and 10 pieces.

But they will not be equal and will not be sectors, they will be different shapes.

Let me know if there is a way to get more than 10 with 4 straight line cuts.

If I had to share the pancake, I'd want to do the cutting. ;)

Think about the placement of the last cut.
The OP does not requre them to be equal size.
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with 4 straight line: 11 pieces.

Generalized: if n is the number of lines and f(n) is the number of pieces, then

f(n)=f(n-1)+n;

where, f(0)=1;

results:

0 line--> 1 piece

1 line--> 2 pieces

2 lines --> 4 pieces

3 lines--> 7 pieces

4 lines--> 11 pieces

5 lines--> 16 pieces

6 lines-->22 pieces

:

:

Edited by storm
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If I had to share the pancake, I'd want to do the cutting. ;)

Think about the placement of the last cut.
The OP does not requre them to be equal size.

Got it. 11 pieces it is. Wow ...shows that I know lesser than I thought I knew about functions.

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Using a knife to make four straight-line cuts,

how many pieces can a single pancake be divided into?

Generalize for N cuts.

Roll the pancake first (actually after adding the sugar lemon and berries - heck just eat it)

If you don't eat it but cut it four times first - then in a rolled condition how many pieces do you get!

I guess size matters!

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Hi storm. Can you show your answer graphically like what chanakyavq did? hheh

here u go. if you notice the pieces are not equal and some are very small. but according to the problem, it does not mention that they need to be equal. So we get 11 pieces.

post-5551-1206285384_thumbgif

Edited by chanakyavg
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Not as good as previous with 16, but 14 by cutting pancake similar to the way guy with four cuts did before (remove 1 o'clock to 8 o'clock cut), gets you 7 pieces. Then cut into top and bottom and you have 14 pieces.

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Hi storm. Can you show your answer graphically like what chanakyavq did? hheh

I have already shown the generalized form...for graphical...cilck spoiler

Here it is..

pancakeid4.jpg

Edited by storm
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Here is my answer

with four cuts we can get 14 pieces. It goes like

1 cut 2 pieces

2 cut 4 pieces

3 cut 7 pieces

4 cut 14 pieces(cut from side)

5 cut 25 pieces(again from side but slightly angeled)

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