# Curve Data: A-hint for A-thin

I just recently know about Curve Data puzzles from Logic Masters India. Here I tried to write two simple puzzles to introduce them to you. They should be easy though as I still can't write a harder one.

Rules of Curve Data:

• Make some figures by drawing lines through the centre of cells so that each figure goes through just one clue.
• All cells are visited by lines.
• A clue shows how the line passing through it turns and connects with itself, without any rotation or reflection.
• However, the clue does not specify length of each straight segment of the line in any way - the lengths of straight segments may vary, but must not be 0.
• Here is a small example:

And here are the two puzzles.

Due to the nature of the puzzle, guessing is really possible. Thus, the answer without logical deduction here is discouraged. The (mobile-friendly) web interfaces are also available here and here.

Full credit to @AxiomaticSystem for this answer (2nd problem). I'm just writing my personal logical deductions. Apologies for how long this is; I can make deductions but struggle to explain them succintly.

First off, let's figure out the vertical line. If it goes down, then we must consider how to fill the space next to it (2 to the left of the n). The only options are the t and the n. If it's the t, then it is part of the curvy bottom bit. The t's trunk is forced into that column, and with the curve and horizontal line there isn't any room for the n (picture to prove it:)
If we attempt to force the n into that spot, then there are empty spaces in between the two vertical lines, so that is impossible. (around this point I realized that I couldn't take pictures of all of the steps. Also, the timer on the web version was freaking me out, so the rest of the pictures are drawings on a screen shot)
So the vertical line must go up only. There are also some other lines forced. The t's letter must be on its right tip. Proof: It can't be on the top tip (can't go down), left tip (can't go right), bottom curve (can't go far enough up). The n's right line must go all the way up, since no other letter can reach the spot below the horizontal line. Then it has to go horizontal for at least 1, forcing the horizontal line to also go horizontal. So now the board looks like this:
Now turn your attention to the third column from right. It can be filled by the swirl, the t's trunk, the t's bottom curve, or the n. It can't be the n, that would leave empty spaces. It can't be the t's trunk, that leaves no space for the n. It can't be the t's bottom curve because then the four top-row spaces above the t cannot be filled. If one's filled by the bottom curve, then only one more can be filled by the t's top tip. If one is filled by the tip, no letter can reach to the space on the left of it. If none are filled by the tip... that doesn't work, there needs to be a tip. So it's impossible. If that explanation made no sense, look at the picture and try to fill the spots above the t.
So that column (3rd from right, remember?) has to be filled by the spiral swirl thing. To reach it, the spiral must curve around the edges. (has to avoid the h, t, and vertical line)
Now look at the h. Its long side has to be at least 3 long, so it extends into the available space. Then its shorter leg must be in the column next to its long side, or there would be unreachable space in between the legs (like there was with the n). So the h must look like this:
Now it's fairly trivial to figure out where the t's curve goes, which forces its trunk into the 4th-from-right column. Once the t is in place, the spiral just takes up the rest of the space

That was long. But there you have it: logical deductions for problem #2.

• I didn't expect this long, but there you go, great explanation! Checkmark awarded here :D May 29, 2020 at 22:57
• Thanks! My brain, it seems, does not like shortcuts. May 29, 2020 at 23:01

Solution to the first puzzle:

Reasoning:

The leftmost column of the A must be at least three cells tall, so it cannot be the column A is in and must be the leftmost one. Similarly, H's leftmost column is the one H appears in, so A must fill the entire left column. H must be two cells wide, because otherwise there would be an unfillable cell between its legs.

We draw our attention to the cells to the left of I. T cannot reach far enough left to fill them, and N could not fill them either: either there is no room for A's right leg or there is an unfillable gap near T and another in the right half of N.

So A must enclose H. T still cannot fill to the left of I, so N must - since there is only one column of space it must go over I to do so. T is forced into the gap in the right half of N, and the dash fills the remaining space.

The other puzzle, although I ran into so many dead ends along the way that I don't have an established line of reasoning for it yet:

• To give you a nudge for the second puzzle, observe the speciality of "t" clue, :) May 27, 2020 at 23:40
• I know that I can show that rot13(gur fgrz bs gur "g" zhfg nccrne gb gur yrsg bs "v") but the rest still feels handwavey May 28, 2020 at 0:25
• Further hint: rot13("g" unf rzcgl pbearef ba vgf hccre yrsg naq evtug, lbh pbhyq qb fbzrguvat r.t. hccre yrsg pbeare pna bayl or svyyrq ol "n") :) May 28, 2020 at 4:37