FORTNIGHT'S PUZZLE 14

PUZZLE 14: 26th April - 2nd May (to be e-mailed by the 3rd May)
POSTED BY IES CAMPANAR

A CHESS GAME
There were 15 players in the latest chess game in which Kazimier Kaczyinski took part following the Swiss variant (all-against-all, once).The sum of all the points obtained by all the players except Kazimier was: 100 points. How many points did Kazimier get?

Note: 1 point for a win and ½ for a draw, each player.

SOLUTION
First of all we can argue that each person plays against the other 14 players, so the number of games should be 15x14. However, if we do it this way, each game is counted twice. This is why the total number of games is actually (15x14)/2 = 105.Since each game means 1 point of the total amount, we would have as a result 105 points.Consequently Kazimier got 105 – 100 = 5 points.