Problem #PRU-66096

Problems Number theory Numeral systems

Problem

Detective Nero Wolf investigates a crime. He’s got 80 people involved in the case, among whom one is a criminal and another is a witness to the crime (but it is not known who either of them are). Each day the detective may invite one or more of these 80 people, and if there is a witness among those invited, but not the perpetrator, the witness will report who the perpetrator is. Can the detective solve a case in 12 days?