October 2018 - Page 2

LaurV · 2018-10-06, 03:41

Hm... according with what the talk is talking here, I may have to waste my weekend playing with triangles... (didn't start yet, but it is really tempting!)

axn · 2018-10-06, 04:09

Quote:

Originally Posted by bsquared

(on the max-sized grid)

There is no "the" max-sized grid, right? If I'm not mistaken, these are the allowable grids (of points).

Code:

a1call · 2018-10-06, 04:27

Quote:

Find a solution for N=11 and the L1*L2<=600.

Largest near square grid is a matrix of 25x24=600
Largest maximally elongated possible grid is a matrix of 6x100.

For 6 <= L1 <=100
L2 <= 600\L1

axn · 2018-10-06, 04:34

Quote:

Originally Posted by a1call

Largest near square grid is a matrix of 25x24=600
Largest maximally elongated possible grid is a matrix of 6x100.

For 6 <= L1 <=100
L2 = 600\L1

Right, that's the length of the grid. I'm talking about the points. n points x m points = (n-1) length x (m-1) length

Also, for placing N points successfully, you'll need at least (N-1) points x (N-1) points grid.

a1call · 2018-10-06, 04:41

There are only 11 points placed on a grid with a maximum of 600 cells. Any 3 point subset of the 11 points forms a triangle. There are 165 different 3-combinations of 11 points, forming 165 triangles none of which may have the same area as any other.

bsquared · 2018-10-06, 05:53

Quote:

Originally Posted by axn

There is no "the" max-sized grid, right? If I'm not mistaken, these are the allowable grids (of points).

Code:

Yes, you're right. I used L1,L2 = 23,26, corresponding to your 24x27 grid of points. I haven't tried the more elongated ones yet, maybe I should.

Best solution so far is now at 163 on the dimension 23x26 grid.

LaurV · 2018-10-06, 08:15

Scratch that! I am stupid! (I thought I solved it)

(advantages of being supermod, haha, can remove posts where my mouth was talking without me...)

Batalov · 2018-10-07, 02:02

It is a fun puzzle!
A solution for n points contains n (n-1)-point solutions in it.

Without the L1*L2<=600 constraint it is easy to find a sparse set, e.g.
[[26,11], [32,10], [0,24], [17,0], [34,6], [32,18], [2,14], [31,2], [7,3], [21,25], [10,25]]

Now, need to tighten the cage...

Batalov · 2018-10-07, 15:57

Tightening the solution "from above".

I have a few S=700 solutions, S=663 and an S=644 solution...

a1call · 2018-10-07, 19:30

Just not to have misdirected anyone, it's not clear to me if the grid size of L1xL2<=600 is based on the L's being counted from 0 or 1.
If the former then an actual grid cell number of 26x25=650 or less would be valid.

Batalov · 2018-10-07, 19:36

Quote:

Originally Posted by a1call

Just not to have misdirected anyone, it's not clear to me if the grid size of L1xL2<=600 is based on the L's being counted from 0 or 1.
If the former then an actual grid cell number of 26x25=650 or less would be valid.

It is perfectly clear when you follow the worked example for (note) 3x3 N=4 solution.
Because it uses dots with coordinates ranging from 0 to 3, you have your answer right there.

It is like a Go board: for which the grid has only 18x18 squares (in terms of this IBM problem, its area is 324), but you can use 19x19 positions to put a stone!

2018-10-06, 08:15	#18
LaurV Romulan Interpreter Jun 2011 Thailand 9611₁₀ Posts	Scratch that! I am stupid! (I thought I solved it) (advantages of being supermod, haha, can remove posts where my mouth was talking without me...) Last fiddled with by LaurV on 2018-10-06 at 08:19

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2018-10-06, 03:41	#12
LaurV Romulan Interpreter Jun 2011 Thailand 10010110001011₂ Posts	Hm... according with what the talk is talking here, I may have to waste my weekend playing with triangles... (didn't start yet, but it is really tempting!)

2018-10-06, 04:41	#16
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 4007₈ Posts	There are only 11 points placed on a grid with a maximum of 600 cells. Any 3 point subset of the 11 points forms a triangle. There are 165 different 3-combinations of 11 points, forming 165 triangles none of which may have the same area as any other.

2018-10-07, 02:02	#19
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	It is a fun puzzle! A solution for n points contains n (n-1)-point solutions in it. Without the L1*L2<=600 constraint it is easy to find a sparse set, e.g. [[26,11], [32,10], [0,24], [17,0], [34,6], [32,18], [2,14], [31,2], [7,3], [21,25], [10,25]] Now, need to tighten the cage...

2018-10-07, 15:57	#20
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3⁶·13 Posts	Tightening the solution "from above". I have a few S=700 solutions, S=663 and an S=644 solution...

2018-10-07, 19:30	#21
a1call "Rashid Naimi" Oct 2015 Remote to Here/There 3·5·137 Posts	Just not to have misdirected anyone, it's not clear to me if the grid size of L1xL2<=600 is based on the L's being counted from 0 or 1. If the former then an actual grid cell number of 26x25=650 or less would be valid.