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MathNet 2005 — Part 02 Question 96

Math Olympiad Vault · MathNet 2005 — Part 02

Question 96

Ivo writes consecutively the integers $1, 2, \ldots, 100$ on 100 cards and gives some of them to Yana. It is known that for every card of Ivo and every card of Yana, the card with the sum of the numbers on the two cards is not in Ivo and the card with the product of these numbers is not in Yana. How many cards does Yana have if the card with number 13 is in Ivo?