Ovotovata Fillomino
(Published on 7. September 2020, 13:42 by spxtr)
Modified fillomino rules:
- Divide the grid into orthogonally connected regions.
- Each cell must contain a number equal to the number of squares in its region.
- No two regions of same size may share an edge.
- All monominos are given.
Modified ovotovata rules:
- Draw a single undirected closed loop through the centers of cells that passes through every region exactly once.
- The loop may not branch off or intersect itself.
- The loop will exit each region twice. After at least one of these exits it must go straight and then turn on the nth cell, where n is the size of the region.
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!
Solution code: Rows 9 and 10.
Comments
on 9. November 2022, 14:08 by polar
A lovely & original puzzle thank you! I too fell into the same trap as others :)
on 18. September 2021, 13:58 by Mark Sweep
Very cool puzzle! Tricky at times, but with great logic and fun!
edit: Glad you liked it :) -spxtr
on 28. October 2020, 07:51 by spxtr
Thanks for the kind words, MagnusJosefsson :)
on 27. October 2020, 11:54 by MagnusJosefsson
Wow, absolutely wonderful! Quite a few "aha" moments when finally finding the way forward after wondering if I made a mistake. Very rewarding finish as well.
on 22. September 2020, 17:22 by 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.
on 8. September 2020, 12:12 by spxtr
Thanks for sticking it out despite the confusion with the rules. I'll update the example tomorrow. Glad you liked the puzzle!
on 8. September 2020, 10:14 by 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.
on 8. September 2020, 09:37 by spxtr
Removed that the loop cannot touch itself. You're absolutely right that I was misusing the word. Sorry for the confusion there.
It is a little difficult to describe, but I was thinking of a difference between touching and intersecting before. Touching would be if the line enters a cell and then turns, then later enters the same cell from a different direction and turns again. In my head, this wasn't an intersection since it's not actually crossing over itself. I think the current rules suffice, feel free to suggest an alternative.
on 8. September 2020, 09:19 by Dandelo
And if this is true, what is the difference between touching and intersecting?
on 8. September 2020, 09:16 by 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.
on 8. September 2020, 07:23 by 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.
on 7. September 2020, 19:56 by 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.
on 7. September 2020, 17:16 by Dandelo
@CHalb: You count one entry and one exit, he counts two exits, since it is undirected.
on 7. September 2020, 16:46 by CHalb
Does the loop enter and exit each region twice or only once as in the example?
on 7. September 2020, 14:28 by 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...
