I had never considered writing a balance loop until now. This is a triple-themed balance loop - no clues on the edges, antisymmetry, and odd clues on blacks, even on whites.
Rules: Draw a closed loop passing through centres of cells horizontally or vertically. 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.
Edit: A number added to R6C4, and a circle added to R6C3, to fix uniqueness issue.
Rules: Draw a closed loop passing through centres of cells horizontally or vertically. 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.
Edit: A number added to R6C4, and a circle added to R6C3, to fix uniqueness issue.
Multiple solutions here.
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