imqwerty
  • imqwerty
yo (⌐■_■)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
ali2x2
  • ali2x2
yo (⌐■_■)
anonymous
  • anonymous
Herro
imqwerty
  • imqwerty
http://prntscr.com/85qp9w

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imqwerty
  • imqwerty
@Empty @dan815
dan815
  • dan815
|dw:1439845105204:dw|
dan815
  • dan815
|dw:1439845339882:dw|
dan815
  • dan815
|dw:1439845520781:dw|
Empty
  • Empty
It might help to start at this configuration and then manipulate this to get other forms too:|dw:1439845619600:dw| But yeah idk other than just rearranging within these diagonals we still won't cover all of them, cause like you've shown @dan815 we have some others.
dan815
  • dan815
the arragenment u have there is also since its increasing wrt to the sum of the indices too
dan815
  • dan815
how about a coming with bounds like
dan815
  • dan815
difference of 2 cannot exist for top and bottom
dan815
  • dan815
|dw:1439845851729:dw|
dan815
  • dan815
as 2 cannot be placed so we know that one side must always have a +1 to it
dan815
  • dan815
now its about the separation that is possible we can have 1 side with +1 and the other side can go up to a max of the row length i think
Empty
  • Empty
Hmmm one bound I see is that for a 3x3 matrix we have: \(b_1 \ge 1\), \(b_2 \ge 3\), \(b_3 \ge 1\)
dan815
  • dan815
lets come back to this -.- lets do this http://prntscr.com/85qvgt
Empty
  • Empty
Hmmm I think this is related to triangular numbers isn't it?
dan815
  • dan815
its all related to something alright
dan815
  • dan815
how about building it up from smaller, like whats the max intersections for 3 lines, are there some number of intersections not possible
Empty
  • Empty
3 lines either intersect 0, 1, 2, or 3 times.
dan815
  • dan815
okay right and for this question 0 is not possible becase of the no 3 concurrent rule
dan815
  • dan815
how does that scale with more lines
Empty
  • Empty
Is that what concurrent means? Parallel?
dan815
  • dan815
ya i googled it one of the synonyms said parallel so i went with it lol
imqwerty
  • imqwerty
yes concurrent = parallel
dan815
  • dan815
it was written by some dude that had a notion of a line
Empty
  • Empty
Waste of a word imo
dan815
  • dan815
hehehe
Empty
  • Empty
Then 3 lines must intersect: 1 or 3 points only.
Empty
  • Empty
|dw:1439847255272:dw|
dan815
  • dan815
wait 2 is possible since we are allowed 2 concurrent just not 3
Empty
  • Empty
Oh ok
dan815
  • dan815
how about we just try to figure that out for a 100 lines, how many lines can be have with same slopes or not same slopes
dan815
  • dan815
the least number of slopes present can be 50 the max is 100 then we can consider the different intercepts vs same intercepts
dan815
  • dan815
now the problem looks more algebraic
dan815
  • dan815
the case of the 3 line intersections can be broken down into number of different slopes number of different intercepts to determine the number of intersections
dan815
  • dan815
f(m,b)=intersections(m,b) the number of intersections is some function of the the different number of slopes m and the different number of intercepts b lets try to come up with an equation like this one
dan815
  • dan815
we can be solving like a general problem then!
dan815
  • dan815
f(n,m,b)=intersections(n,m,b) let n be the number of lines m be the number of unique slopes b be the number of unique intercepts
dan815
  • dan815
the last one doesnt make sense, i dunno but something like this
ali2x2
  • ali2x2
lol eggheads
dan815
  • dan815
how about this different slopes and different intersections points like how 3 slopes must not share the same slope, and no 3 lines can share the same intersection point
dan815
  • dan815
y-y1 = m1*(x-x1) let there be 100 lines of this form max number of mi =2 and we can see the max number of (xi,yi)s so that 2002 intercsecs exist or if possible
dan815
  • dan815
base case all same (xi,yi) means everything has different slope and 1 intersetion for 1 same slope, we must have atleast 1 different (xi,yi), other wise a line would coincide and we have infinte intersections

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