Number theory · Divisors of an integer · Integer constraints · Scoring invariant
Nika and Tim played a series of card games. A draw was impossible. They agreed in advance that after each game the winner receives more points than the loser and that the loser receives a positive number of points, and they fixed exactly how many points the winner and the loser get. After some number of games Nika had \(30\) points, while Tim, who had won \(2\) of the games, had \(25\) points. How many points did the winner of an individual game receive?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2004, 1. letnik, category A, problem 5. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source