TOT 2004 Spring - Senior A-Level p6 audience shuffles a deck of 36 cards
Source:
February 25, 2020
combinatorics
Problem Statement
The audience shuffles a deck of cards, containing cards in each of the suits spades, hearts, diamonds and clubs. A magician predicts the suit of the cards, one at a time, starting with the uppermost one in the face-down deck. The design on the back of each card is an arrow.
An assistant examines the deck without changing the order of the cards, and points the arrow on the back each card either towards or away from the magician, according to some system agreed upon in advance with the magician. Is there such a system which enables the magician to guarantee the correct prediction of the suit of at least
(a) cards;
(b) cards?