Physical zero-knowledge proof and NP-completeness proof of Suguru puzzle

Suguru is a paper and pencil puzzle invented by Naoki Inaba. The goal of the game to fill grid with numbers between 1 5 while respecting three simple constraints. We first prove NP-completeness puzzle. For this we design gadgets encode PLANAR-CIRCUIT-SAT in grid. then physical Zero-Knowledge Proof (ZKP) protocol for Suguru. This ZKP allows prover that he knows solution verifier without leaking any information on solution. To construct such protocol, only rely few cards adapted encoding. n cells, use 5n+5 cards. Moreover, classical security properties ZKP: completeness, extractability, zero-knowledge.