The Hamiltonian Circuit 149

Embark on a quest to traverse each square within the grid without colliding with barriers or retracing your steps, aiming to establish an uninterrupted circuit.

To initiate your journey, commence with the elementary 4x4 configurations. Deliberate each move meticulously, looking multiple steps ahead. Should you sense an error, retrace your path; it will vanish.

If you encounter a perplexing juncture, access the Hints feature. Missteps will be highlighted in red before vanishing. Conversely, when on the correct route, a new segment will materialize.

Each puzzle boasts a singular solution. Upon its discovery, recognition will be immediate.

Commencing from 4x4 matrices and broadening to 20x20 challenges, the larger conundrums pose formidable tests, potentially spanning hours of deliberation. If necessitated to cease mid-puzzle, rest assured that progress is automatically preserved.

For some, engagement with these circuits fosters a meditative state; for others, it may induce cerebral exertion. Regardless of your inclination, engage in enhancing your abstract cognizance and challenging your mind in significant ways.

Drawing inspiration from the ingenious puzzle devised by Irish mathematician William Rowan Hamilton in 1856, these circuits initiate gently but ramp up to formidable complexity. Best of luck!

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