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For a set of four distinct lines in a plane, there are exactly N disti

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For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 14 May 2019, 00:24
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  85% (hard)

Question Stats:

19% (01:32) correct 81% (01:58) wrong based on 32 sessions

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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 14 May 2019, 01:11
Maximum value of N can be 6. Hence sum of all possible values of N is 21. 6*7/2

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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 14 May 2019, 08:46
rupam : can you please explain much more?

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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 14 May 2019, 09:31
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kunalbean The maximum no of intersecting points for N different lines on a plane is (N^2-N)/2. In this case N=4; So maximum no of intersecting points is (16-4)/2=6. And the least no of intersecting points is 0(Considering all 4 parallel). So summation is 6+5+4+3+2+1+0=21
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 15 May 2019, 09:36
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@rupampaul : thank you for the response!
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 16 May 2019, 09:59
RupamPaul13 wrote:
kunalbean The maximum no of intersecting points for N different lines on a plane is (N^2-N)/2. In this case N=4; So maximum no of intersecting points is (16-4)/2=6. And the least no of intersecting points is 0(Considering all 4 parallel). So summation is 6+5+4+3+2+1+0=21



From where this formula originates...Do you have any details to refer and understand?
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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 29 Nov 2019, 09:36
Someone please solve and share your approach to this question.

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Re: For a set of four distinct lines in a plane, there are exactly N disti  [#permalink]

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New post 29 Nov 2019, 09:53
Case 1 all lines meet at the same point. =1
Case 1a try to make 2 not possible
Case 2 3 parallel = 3
Case 3 2 sets o parallels = 4
Case 4 parallel 2 not with independent intersection = 5
Case 5 all independent = 6
Case 6 all parallel 0
0+1+3+4+5+6=19

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Re: For a set of four distinct lines in a plane, there are exactly N disti   [#permalink] 29 Nov 2019, 09:53
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