## Equality

(Eingestellt am 23. März 2020, 09:51 Uhr von Puzzle_Maestro)

This is a puzzle type that first appeared at the 2019 WPC, and I thought it was interesting enough to make a puzzle on!

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)

Lösungscode: Die Anzahl der Felder, in denen der Rundweg abknickt, zeilenweise von oben nach unten.

Zuletzt geändert am 23. März 2020, 14:13 Uhr

Gelöst von uvo, JonaS2010, ropeko, Feadoor, Zzzyxas, moss, matter, skywalker, cdwg2000, rimodech, NikolaZ, Joe Average, marcmees, Statistica, karzym, bob, HaSe, Circleconstant314, ManuH, pirx, Ours brun, Realshaggy, ch1983, amitsowani, tuace, zorant, Uhu, ibag
Komplette Liste

### Kommentare

am 1. April 2020, 19:12 Uhr von tuace
Really nice. It is always exciting to see what other authors do with my puzzle inventions :)

am 25. März 2020, 00:13 Uhr von HaSe
really great puzzle

am 23. März 2020, 17:08 Uhr von 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.

Zuletzt geändert am 23. März 2020, 16:45 Uhr

am 23. März 2020, 16:43 Uhr von 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?

am 23. März 2020, 15:05 Uhr von JonaS2010
Very nice!

am 23. März 2020, 14:03 Uhr von Puzzle_Maestro
Fixed multiple solutions. Thanks to uvo for pointing it out.

 Schwierigkeit: Bewertung: 96 % Gelöst: 28 mal Beobachtet: 0 mal ID: 00039O

Lösungscode: