yo (⌐■_■)

- imqwerty

yo (⌐■_■)

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- ali2x2

yo (⌐■_■)

- anonymous

Herro

- imqwerty

http://prntscr.com/85qp9w

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## More answers

- imqwerty

@Empty @dan815

- dan815

|dw:1439845105204:dw|

- dan815

|dw:1439845339882:dw|

- dan815

|dw:1439845520781:dw|

- 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

the arragenment u have there is also since its increasing wrt to the sum of the indices too

- dan815

how about a coming with bounds like

- dan815

difference of 2 cannot exist for top and bottom

- dan815

|dw:1439845851729:dw|

- dan815

as 2 cannot be placed so we know that one side must always have a +1 to it

- 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

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

lets come back to this -.-
lets do this
http://prntscr.com/85qvgt

- Empty

Hmmm I think this is related to triangular numbers isn't it?

- dan815

its all related to something alright

- 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

3 lines either intersect 0, 1, 2, or 3 times.

- dan815

okay right and for this question 0 is not possible becase of the no 3 concurrent rule

- dan815

how does that scale with more lines

- Empty

Is that what concurrent means? Parallel?

- dan815

ya i googled it one of the synonyms said parallel so i went with it lol

- imqwerty

yes concurrent = parallel

- dan815

it was written by some dude that had a notion of a line

- Empty

Waste of a word imo

- dan815

hehehe

- Empty

Then 3 lines must intersect:
1 or 3 points only.

- Empty

|dw:1439847255272:dw|

- dan815

wait 2 is possible since we are allowed 2 concurrent just not 3

- Empty

Oh ok

- 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

the least number of slopes present can be 50
the max is 100
then we can consider the different intercepts vs same intercepts

- dan815

now the problem looks more algebraic

- 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

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

we can be solving like a general problem then!

- 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

the last one doesnt make sense, i dunno but something like this

- ali2x2

lol eggheads

- 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

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

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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