Equality
(Published on 23. March 2020, 09:51 by Puzzle_Maestro)
Draw a closed loop into the grid that runs horizontally and vertically and passes through each cell at most once. The loop must enter and leave each region at least twice. For multiple visits of the same region, each visit must pass through the same number of cells. That number can be equal or different for different regions. If a region contains a number, that number indicates how many cells in that region are not used by the loop. Grey cells cannot be used by the loop, and they are not part of any region. (there are none in this puzzle)
Solution code: Enter the number of times the loop turns in each row from top to bottom.
Comments
on 21. January 2022, 12:27 by Vebby
Link to solve on Penpa+ with answer check (green lines):
https://tinyurl.com/yvh9hhwk
on 29. July 2020, 21:27 by dm_litv
Very nice!
on 27. July 2020, 09:21 by CHalb
After solving and enjoying this puzzle very much I recommended it to my son. We did it together and he explicitly said some times during solving, that this is a great puzzle for him, too.
on 1. April 2020, 19:12 by tuace
Really nice. It is always exciting to see what other authors do with my puzzle inventions :)
on 25. March 2020, 00:13 by HaSe
really great puzzle
on 23. March 2020, 17:08 by Puzzle_Maestro
Your initial assumption is correct. If one visit of a region uses X cells, all subsequent visits must also use X cells.
‘Enter and Leave’ mean exactly what you’d expect them to: crossing the boundaries of the region. Hence, the loop must indeed cross the boundary of each region at least 4 times.
on 23. March 2020, 16:43 by Circleconstant314
I'm a little bit confused here. If a region is visited only twice, are the number of visited cells per visit still the same? Similarly, if during one visit of a region the loop uses X cells, does this mean any future visits of that same region must use exactly X cells and no more or fewer?
EDIT: Also, what does "enter and leave" mean here? Does the sentence "enter and leave each region at least twice" mean that the loop must cross over the boundary of each region at least four times?
on 23. March 2020, 15:05 by JonaS2010
Very nice!
on 23. March 2020, 14:03 by Puzzle_Maestro
Fixed multiple solutions. Thanks to uvo for pointing it out.
