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M19-22

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Bunuel
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M19-22 [#permalink] New post   16 Sep 2014, 01:06
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Question Stats:

27% (01:06) correct 73% (01:17) wrong based on 220 sessions
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What is the maximum number of pieces that a circular pie can be divided into by making four linear cuts?

A. 6
B. 8
C. 9
D. 10
E. 11
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E
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Bunuel
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Re M19-22 [#permalink] New post   16 Sep 2014, 01:06
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Official Solution:

What is the maximum number of pieces that a circular pie can be divided into by making four linear cuts?

A. 6
B. 8
C. 9
D. 10
E. 11


To solve this type of combinatorial problem, pattern recognition is often the key.

Maximum pieces:

0 cuts result in 1 whole piece;

1 cut will produce 2 pieces: \(1 + 1 = 2\);

2 cuts will produce 4 pieces: \(2 + 2 = 4\);

3 cuts will produce 7 pieces: \(4 + 3 = 7\);

4 cuts will produce 11 pieces: \(7 + 4 = 11\).

Following the same pattern:

5 cuts will produce 16 pieces: \(11 + 5 = 16\);

6 cuts will produce 22 pieces: \(16 + 6 = 22\);

7 cuts will produce 29 pieces: \(22 + 7 = 29\).

In general, the \(k_{th}\) cut will add \(k\) new pieces.

Thus, with four linear cuts, a circular pie can be divided into a maximum of 11 pieces.




Answer: E
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buddyisraelgmat
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Re: M19-22 [#permalink] New post   01 Apr 2015, 10:06
WOW !

This problem is a really smartly designed !

Got it wrong though :|
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aimtoteach
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Re: M19-22 [#permalink] New post   25 Sep 2015, 13:20
Hello Bunuel

Could you please help me with this one - I didn't understand the explanation.
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happyface101
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Re: M19-22 [#permalink] New post   18 Jan 2016, 12:34
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aimtoteach wrote:
Hello Bunuel

Could you please help me with this one - I didn't understand the explanation.


Not sure if this is still helpful to you ... it's been a few months since you posted the question, but here is some clarify:

1 line: 1+1 = 2 pieces -- straight forward
2 lines: carry the 2 pieces from the last one + 2 lines = 4 pieces
3 lines: carry the 4 from the last one + 3 lines = 7 pieces
4 lines: carry the 7 from the last one + 4 lines = 11 pieces


Hope this helps you!
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sanghar
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Re: M19-22 [#permalink] New post   22 Aug 2016, 09:47
Nice question/solution Bunuel, got it by drawing the figure though :p
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Senthil7
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Re: M19-22 [#permalink] New post   23 Aug 2016, 05:33
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I think this is a high-quality question and I agree with explanation.
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Re: M19-22 [#permalink] New post   05 Sep 2016, 11:01
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Although answered incorrectly, I liked this question after reading the solution. Can someone post such similar questions? Thanks!

I believe this is true for any shape, need not necessarily be a circle? Am I correct?
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arvind910619
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Re: M19-22 [#permalink] New post   03 Jul 2018, 08:10
wow this problem is really good for maximum pieces we have to divide the pie into unequal parts and make sure that lines do not pass through intersection points. Then we will maximum pieces.
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CAMANISHPARMAR
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Re: M19-22 [#permalink] New post   08 Oct 2018, 22:18
Attachment:
Circle With lines.jpg
Circle With lines.jpg [ 71.76 KiB | Viewed 16409 times ]


There is nothing much one can do when you draw the first line. The circle will be divided intwo two parts.

When you draw the second line then you have a choice, either you can interest the first line or not? Obviously when the second line intersects the first line within the circle then you have more divisions, i.e. 4 in all.

So one can learn from step two to draw the third line which will intersect as many lines as possible within the circle. I.e. third line intersecting the first two lines. Similarly the fourth line intersecting the first three lines, giving us 11 parts.
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Mrjack
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Re: M19-22 [#permalink] New post   12 Apr 2019, 06:48
:cry: this question ..... is just too much of a trap
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Re: M19-22 [#permalink] New post   09 Jul 2021, 02:35
good question
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Bunuel
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Re: M19-22 [#permalink] New post   04 Feb 2024, 11:25
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M19-22 [#permalink]
04 Feb 2024, 11:25
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Bunuel
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