TL;DR
Rikudo, a puzzle involving completing a Hamiltonian path on a hexagonal grid, is NP-complete in general, but solvable in polynomial time when all odd numbers are placed, with certain variants remaining NP-hard.
Contribution
The paper proves that Rikudo is NP-complete in general and identifies specific cases where it is solvable in polynomial time or remains NP-hard.
Findings
Rikudo is NP-complete even without holes.
When all odd numbers are placed, Rikudo is in P.
It remains NP-hard when all numbers of the form 3k+1 are placed.
Abstract
Rikudo is a number-placement puzzle, where the player is asked to complete a Hamiltonian path on a hexagonal grid, given some clues (numbers already placed and edges of the path). We prove that the game is complete for NP, even if the puzzle has no hole. When all odd numbers are placed it is in P, whereas it is still NP-hard when all numbers of the form are placed.
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