A gallery of classic NP-complete decision problems. Each comes with a small and a medium example, as a Yes instance and as a No instance. Click into the drawing to build a candidate certificate; the verifier on the right checks it against the definition, in polynomial time. For Yes instances, a certificate can be revealed; for No instances, a short argument (and an exhaustive search) explains why no certificate can exist. All inputs can be edited in a plain text format.