Modified fillomino rules:
Modified ovotovata rules:
These rules are based on a puzzle type by Eric Fox, but they're modified so make sure you read them carefully. I've given an example 5x5 below, with a valid solution on the right. Note that the "go straight then turn" rule only needs to apply to one of the exits, not both. So the 4 region in row 1 columns 1-4 has two exits to row 2: one in column 1 and one in column 3. In only column 1 does the loop continue for 4 squares before turning. Note as well that it may pass through orthogonally connected cells as long as it does not cross itself.
The puzzle is below, and here's the penpa. Please do leave a comment and a rating if you manage to solve it. The start is a little tricky, especially since you're grappling with new rules. I'm happy to give a hint if you're stuck, so feel free to ask in the comments. Don't forget that you can't place any additional 1s!
Lösungscode: Rows 9 and 10.
am 22. September 2020, 17:22 Uhr von Dandelo
@jessica: Wenn du das Problem genau in der Mitte hast und unten noch was fehlt, bist du an einer Stelle, an der ich auch kurz stecken geblieben bin. Ich erinnere mich noch grob, dass da doch noch irgendwas ging, was ich zuerst verworfen habe.
am 8. September 2020, 12:12 Uhr von spxtr
Thanks for sticking it out despite the confusion with the rules. I'll update the example tomorrow. Glad you liked the puzzle!
am 8. September 2020, 10:14 Uhr von Dandelo
I think it's ok now. Maybe an alternative is
"enters each cell at most once". The easiest way is probably a picture, e.g. in the example.
But a very nice puzzle anyway.
am 8. September 2020, 09:19 Uhr von Dandelo
And if this is true, what is the difference between touching and intersecting?
am 8. September 2020, 09:16 Uhr von Dandelo
But then it touches itself. r9c9 and r10c9 are orthogonally adjacent.
I think that you don't see this as touching, but usually for touching the whole cells are considered, not the handwritten loop.
Maybe it would be better to show this in the example.
am 8. September 2020, 07:23 Uhr von ropeko
I still don‘t get how the 1 in the corner can fulfill the rules. It has to go straight and turn in the 1st cell. This would mean that the loop will go to r9c9. But then the loop touches itself.
@ropeko: Correct, the loop must go into r9c9. However, it can make a U shape and then go on its merry way. For instance, it can do ... - r9c9 - r9c10 - r10c10 - r10c9 - r10c8 - ..., or similar going the other way.
am 7. September 2020, 19:56 Uhr von spxtr
@Dandelo note that it only needs to obey the "go straight then turn" constraint for one of the exits. This means the 1 in the corner doesn't need to cause the loop to touch itself.
@CHalb I'll update the rules to make this more clear, but Dandelo's response is correct.
@Jesper thanks as always for the kind words, glad you enjoyed it.
am 7. September 2020, 17:16 Uhr von Dandelo
@CHalb: You count one entry and one exit, he counts two exits, since it is undirected.
am 7. September 2020, 16:46 Uhr von CHalb
Does the loop enter and exit each region twice or only once as in the example?
am 7. September 2020, 14:28 Uhr von Dandelo
It seems that I don't understand the rules. It has to turn after leaving the 1 in the corner, but then it touches itself...