TOT 1998 Spring AS6 5 cards from a 52-card deck trick
Source:
May 11, 2020
combinatoricsgamegame strategy
Problem Statement
(a) Two people perform a card trick. The first performer takes cards from a -card deck (previously shuffled by a member of the audience) , looks at them, and arranges them in a row from left to right: one face down (not necessarily the first one) , the others face up . The second performer guesses correctly the card which is face down. Prove that the performers can agree on a system which always makes this possible.
(b) For their second trick, the first performer arranges four cards in a row, face up, the fifth card is kept hidden. Can they still agree on a system which enables the second performer to correctly guess the hidden card? (G Galperin)