# A Code from the Lines

Yeah. I think this puzzle will be the hardest puzzle on Puzzling...

I'll add one hint per 3 days, I'll add a VERY helpful tag on the 3rd week, and I'll post the answer and explanation on the 4th week.

Edit: I've completely managed to ignore this...

Yeah, here's the puzzle: (Thanks to @squeamishossifrage)

This is the correct way to look at it.
All tangents from the positive x are ±0, undef, ±2, ±1/2, ±1.
Find the 3-digit code!!!!!

So, what is the three digit code that is described by these seemingly random lines?

Hint:

This puzzle will have a EUREKA moment, almost like my last puzzle here

Hint 2:

The comments below have a lot of helpful hints, especially the ones on March 27

Hint 3:

Ivo Beckers is missing something else from his picture... For every single one, he has forgotten two lines.

Hint 4:

The EUREKA moment has nothing to do with math.

• Hmmm, a week between every hint? I think that would make the problem not attractive...I'd suggest a hint every 2-3 days if you want this to be solved slowly. – leoll2 Mar 25 '15 at 17:06
• @awesomepi I would request you to add the instruction to your question body. It is very difficult to understand what is written on the paper. ... I agree with "Gosh... I suck at writing" :P – Ashutosh Nigam Mar 25 '15 at 17:12
• @AshutoshNigam There we go – awesomepi Mar 25 '15 at 17:27
• A thing I notice is that the dots along the border never have lines pointing outwards making me think that you have to extend the lines until they reach another dot – Ivo Beckers Mar 27 '15 at 13:23

Try #4

(EDITED to reflect the actual answer, although I went with 342 at first)

Could the 3-digit code be

345

because the path resembles those numbers (see below)

• I hate to say this (no i don't) but your 2nd option is like claiming there's a face on mars. We so desperatly want to see patterns that we see them when they're not there. if you want it to to resemble numbers you have to take all the blocks in account, there are many unused blocks below 2 and cel number 5 ruins your 3 not to mention the squigle inbetween 3 and 4. nicely thought but it is extremely far fetched :P – Vincent Apr 18 '15 at 21:21
• I really like the first part of the puzzle where you have to realize it's a maze. But the way of turning that maze into a 3-digit number feels arbitrary :/ – Lopsy Apr 19 '15 at 5:54
• I showed the final path to my wife and asked her what 3 numbers she saw in it, and she immediately said 345, so I guess it's more of a perspective thing. (I thought it was 342) – JLee Apr 19 '15 at 14:37
• @JLee except in your edited version there is no reasoning for the path you've taken. So it is still unclear why you took this particular path. – Vincent Apr 20 '15 at 12:16
• I'm gonna go with the face on mars here. I went over some of the possible paths including this one and while the middle sort of looked like an intentional 4 (and in other paths, it looked like an intentional 1), the others were plain daydreams. – namey Apr 21 '15 at 19:54

I think the 3-digit code could be

269

because

the graph that is created when the lines are extended to the next dot, has 269 partitions of different sizes and shapes. (thanks to the picture posted in the question's comments by Ivo Beckers, which was missing a couple lines)

• Actually, in the square directly above the bottom-right, you missed a line, which actually brings the total up to 268. – Joe Z. Apr 12 '15 at 21:10
• And in the second from the top, second from the left, making it 269. – Joe Z. Apr 12 '15 at 21:11
• @Joe Yes! good eye! thanks. I started making the connected graph on my own, but then got lazy and decided to use the one that was posted. – JLee Apr 12 '15 at 21:17
• Only this seems disregard the instruction "read from top-left to bottom right", which suggests to me that the answer should be something that can be read digit by digit, but I don't know. – String Apr 12 '15 at 22:23
• @awesomepi Is this a graph coloring problem? if so, can we get some direction? or a hint? if it's not a graph coloring problem, then what level of mathematics is needed to be able to solve it? i just don't want to waste time on a problem that requires some crazy high amount of math knowledge. – JLee Apr 12 '15 at 23:01

The number is

913

Because

that is the number of different non-self-intersecting paths there are that start in the upper left corner and end in the lower right corner.

Take note that

the graph is directed. Just because you can go from (0,0) to (0,1), doesn't mean you can go from (0,1) to (0,0). (with the single exception of the fourth and fifth cells in the first row, but they were a mistake). This was what Ivo Beckers' illustration was missing; "For every single [line], he has forgotten [to add] two lines [to the end of the current line, to make it into an arrow]."

• No... close, but no. – awesomepi Apr 15 '15 at 17:35
• I posit that it's the number of non-self-intersecting paths that don't end in a single dot. – Joe Z. Apr 15 '15 at 17:43
• I haven't checked, but I suspect that number would be more than three digits long. – Kevin Apr 15 '15 at 17:51

Try #2

I think the 3-digit code is

991

Kevin's answer helped me a lot, although I am still not sure this is the correct answer. The shortest path I could find from top left to bottom right is

1,13,3,28,29,49,63,52,53,66,79,93,105,118,119,120 which sums to 991

To get the numbers above, I numbered each cell from 1 to 120, going first from left to right, then top to bottom.

• crap. i just realized that 5 to 31 is not a path! error due to me working backwards! – JLee Apr 17 '15 at 20:18
• my error is now now corrected! – JLee Apr 17 '15 at 20:40
• Well, nice try, and well crap, I found a typo... God dangit the 79 should not have a path going to 93, but you're on the right track. – awesomepi Apr 17 '15 at 21:11
• There, it's fixed... – awesomepi Apr 17 '15 at 21:16
• I guess with that fix, the number will have more than 3 digits now. So maybe, instead of the shortest path in terms of nodes, are we supposed to take the path that yields the smallest number? – Sebastian Reichelt Apr 17 '15 at 22:40

Try #3

I think the 3-digit code is

216

I made a dial, based on the layout of a clock, that assigns a value to each of the 16 directions away from a cell.

After the last edit to the question, the shortest path (based on summing the values) from the upper left cell to the lower right cell is

• Close, try combining the first half of your path in the earlier answer to the next half of this answer. – awesomepi Apr 18 '15 at 14:29

This might be too simple, but could the code be

107?

That seems to be

the number of dots that can actually be reached from the top-left square (by following the lines in the original picture, not Ivo Beckers' one, i.e. taking directionality into account as noted in Kevin's answer).