### Balance Loop by Prasanna Seshadri

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or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s)

Theme: Clue Symmetry and Logic

Author/Opus: This is the 68th puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: (Standard Balance Loop rules.) Draw a single, non-intersecting loop that passes through all circled cells. All white circles must have equal segment lengths on both sides of the circle before turning. All black circles must have unequal segment lengths on both sides of the circle before turning. Numbers indicate the sum of the segment lengths on both sides of the circle.
Also, see this example:

Answer String: Enter the length in cells of the horizontal loop segments from left to right in the marked rows, starting at the top. If the loop only has vertical segments in the marked row, enter 0. Separate each row’s entry with a comma. This example has the key “11,311”.

Time Standards (highlight to view): Grandmaster = 3:00, Master = 4:00, Expert = 8:00

Solution: PDF

• chaotic_iak says:

03:04.

Interesting new genre. I find it pretty difficult to count the lengths, but I guess it’s just because it’s a first puzzle. It’s fancy to see how the left and bottom part works out very well though with so little clues.

• Carl W says:

Really enjoyable new puzzle. I didn’t realize my original solution was invalid until the website wouldn’t enter it. So I got twice the enjoyment by solving it a second time, (and correctly this time).

Compared to Masyu, I find the rules here more elegant. With Masyu, I’ve always found it slightly inelegant that black circles prevent turns in either adjacent square while white circles require only a turn in at least one adjacent square. That makes the black clues slightly weightier than white in their influence. It also meant that when I was first learning Masyu I had to continually consult the rules to remind myself how things worked exactly.

This genre avoids that imbalance by having the same phrasing rules for white and black with the only difference being “equal” or “unequal”.

I’m curious about the numbers. Would Masyu benefit as a puzzle genre by allowing similar numbers? Would Balance Loop be as fertile a genre as Masyu if puzzles were composed without numbers?

• Thank you for such a detailed feedback. Its funny that Balance Loop avoids imbalance – mission accomplished, I suppose!

As for the numbers, in my opinion, if a Masyu’s length elements correspond to this puzzle’s length elements, then the numbers correspond to the fact that Masyu forces the loop to go straight/turn at circles whereas this puzzle has no such restriction. As a standalone, just length elements can be inadequate unless there are many circles or there is a constraint for the loop to go through all cells, so the numbers might be crowded on a Masyu whereas they were a bit more necessary here to have the clues being descriptive enough in the long run.

• Neelix says:

Very nice, I like it. 🙂

– Neelix

• Para says:

How about using squares and diamonds so I don’t keep drawing straight lines through white circles?

After I overcame that it was nice.

• Grizix says:

So true …

Pretty hard for a first of the genre, but enjoyable.

• Francis says:

Great new puzzle type. Hope to see many more!

• skynet says:

11:32

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