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imqwerty
 one year ago
yo (⌐■_■)
imqwerty
 one year ago
yo (⌐■_■)

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Empty
 one year ago
Best ResponseYou've already chosen the best response.0It 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
 one year ago
Best ResponseYou've already chosen the best response.0the arragenment u have there is also since its increasing wrt to the sum of the indices too

dan815
 one year ago
Best ResponseYou've already chosen the best response.0how about a coming with bounds like

dan815
 one year ago
Best ResponseYou've already chosen the best response.0difference of 2 cannot exist for top and bottom

dan815
 one year ago
Best ResponseYou've already chosen the best response.0as 2 cannot be placed so we know that one side must always have a +1 to it

dan815
 one year ago
Best ResponseYou've already chosen the best response.0now 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
 one year ago
Best ResponseYou've already chosen the best response.0Hmmm 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
 one year ago
Best ResponseYou've already chosen the best response.0lets come back to this . lets do this http://prntscr.com/85qvgt

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Hmmm I think this is related to triangular numbers isn't it?

dan815
 one year ago
Best ResponseYou've already chosen the best response.0its all related to something alright

dan815
 one year ago
Best ResponseYou've already chosen the best response.0how about building it up from smaller, like whats the max intersections for 3 lines, are there some number of intersections not possible

Empty
 one year ago
Best ResponseYou've already chosen the best response.03 lines either intersect 0, 1, 2, or 3 times.

dan815
 one year ago
Best ResponseYou've already chosen the best response.0okay right and for this question 0 is not possible becase of the no 3 concurrent rule

dan815
 one year ago
Best ResponseYou've already chosen the best response.0how does that scale with more lines

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Is that what concurrent means? Parallel?

dan815
 one year ago
Best ResponseYou've already chosen the best response.0ya i googled it one of the synonyms said parallel so i went with it lol

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.1yes concurrent = parallel

dan815
 one year ago
Best ResponseYou've already chosen the best response.0it was written by some dude that had a notion of a line

Empty
 one year ago
Best ResponseYou've already chosen the best response.0Then 3 lines must intersect: 1 or 3 points only.

dan815
 one year ago
Best ResponseYou've already chosen the best response.0wait 2 is possible since we are allowed 2 concurrent just not 3

dan815
 one year ago
Best ResponseYou've already chosen the best response.0how 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
 one year ago
Best ResponseYou've already chosen the best response.0the least number of slopes present can be 50 the max is 100 then we can consider the different intercepts vs same intercepts

dan815
 one year ago
Best ResponseYou've already chosen the best response.0now the problem looks more algebraic

dan815
 one year ago
Best ResponseYou've already chosen the best response.0the 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
 one year ago
Best ResponseYou've already chosen the best response.0f(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
 one year ago
Best ResponseYou've already chosen the best response.0we can be solving like a general problem then!

dan815
 one year ago
Best ResponseYou've already chosen the best response.0f(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
 one year ago
Best ResponseYou've already chosen the best response.0the last one doesnt make sense, i dunno but something like this

dan815
 one year ago
Best ResponseYou've already chosen the best response.0how 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
 one year ago
Best ResponseYou've already chosen the best response.0yy1 = m1*(xx1) 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
 one year ago
Best ResponseYou've already chosen the best response.0base 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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