Magic Trick with the deck
Source: RMO Delhi 2016, P6
October 11, 2016
combinatoricsGame Theory
Problem Statement
A deck of cards is given. There are four suites each having cards numbered . The audience chooses some five cards with distinct numbers written on them. The assistant of the magician comes by, looks at the five cards and turns exactly one of them face down and arranges all five cards in some order. Then the magician enters and with an agreement made beforehand with the assistant, he has to determine the face down card (both suite and number). Explain how the trick can be completed.