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IMSO 2005 Mathematics - International Exploration Question 2

IMSO Maths · IMSO 2005 Mathematics - International Exploration

Question 2

Some people are playing a card game. On the table are fifty cards, numbered 1 to 50, all facing up. Each player is allowed to choose a certain number of cards. The player whose chosen cards have the highest total is the winner. There is only one winner.

What is the lowest possible score that makes a player a sure winner if each player has to choose:
(a) two cards?
(b) three cards?
(c) five cards?