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Hey /sci/, quick question that's been bugging me for the past week or so.
Imagine a 3x3 grid of nodes (I guess, I don't know the exact terminology) as in pic related.
Now, imagine a mouse, cursor, ant, or whatever; it starts at any node, and draws a line to any adjacent node (orthagonal or diagonal).
Going from the starting node to another is a shape of length 1, going from that second node to another is one of length 2, and so forth.
Now, my question is, how many possible variations are able to be drawn, of any length n, within that 3x3 grid if the following rules are observed:
1) no back tracking; a line cannot be drawn coincidentally on another.
2) no crossing; the same node can be drawn to multiple times, but it cannot be drawn from if doing so would "cross" a line or angle made of two drawn lines.
What about of length 4 only? What if the grid was 3x2 (rows and columns)?
I apologize for whatever misuse of terminology is present.
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Also bump, for interest
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don't
stop
bump
ing
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OP here, glad to see someone else is inerested. bump.
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>>7658410
3^(3x3)?
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>>7658410
81.
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>>7658410
And 36. There are 6 points from which only 6 lines can be drawn with the given...some word starting with an a.
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>>7658410
You could (and I mean should) work it out yourself.
This falls under the category of recreational mathematics and you do not need any advanced mathematics to work it out.
Just work out the answer for the 3x3 case, the 2x2 case and do not forget the trivial 1x1 and 0x0 cases. Work out 4x4 just for good measure.
Then spend countless hours figuring out what function arrives to the same answers as you when you plug in the numbers.
I would recommend you treat the function as a one variable function where f(3) would mean f of a 3x3 grid. If you capable of doing that and you are not satisfied then try figuring a two variable function that also calculate 3x2 cases.
The only reason I don't do this is that it is time consuming.
A few tips for your adventure:
I am thinking that it is a recursive function so try to express it first at one
If you want to go really deep into it, after you have the recursive function, try turning it into an algebraic one and then prove it by induction, write a paper about it and get a PhD.
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>>7659540
Within the paradigm given.
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>>7659544
Of course, and I'm sketchhing out all the permutations in my free time, I was just betting that this deals with graph theory or something.
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