Ring Ring Minus One
Ring Ring Minus One is a variation of the standard Ring Ring puzzle, first introduced by Pavel Yarkin in September 2025 as part of the Ring-Ring Rally contest.
The idea began as a playful “finish the puzzle for the author” twist, based on a well-known invariant of Ring Ring: the total number of white cells in a valid solution is always even. By removing a single cell—thus breaking this invariant—the variant initially served as an invitation for solvers to reconstruct what the author “must have intended.”
However, the concept quickly proved more interesting than expected. The intentional ambiguity created by the missing cell disrupts the usual, almost mechanical logic of drawing rectangular corners in Ring Ring. Instead, it forces solvers to think at least one step ahead, considering how the altered parity affects loop construction.
This subtle shift results in a variant that feels familiar yet meaningfully more strategic, adding depth without adding rules.
The idea began as a playful “finish the puzzle for the author” twist, based on a well-known invariant of Ring Ring: the total number of white cells in a valid solution is always even. By removing a single cell—thus breaking this invariant—the variant initially served as an invitation for solvers to reconstruct what the author “must have intended.”
However, the concept quickly proved more interesting than expected. The intentional ambiguity created by the missing cell disrupts the usual, almost mechanical logic of drawing rectangular corners in Ring Ring. Instead, it forces solvers to think at least one step ahead, considering how the altered parity affects loop construction.
This subtle shift results in a variant that feels familiar yet meaningfully more strategic, adding depth without adding rules.
Rules
Draw few rectangular loops through the centers of unshaded cell so that exactly one unshaded cell is unused and all other unshaded cells are used. The sides of different rectangles may intersect each other, but not turn at their intersections or otherwise overlap.
Click to see the answer.