Yesterday evening, Cristiano Ronaldo looked into a newspaper and quickly detected the sports section. After fifteen minutes of reading and studying, Cristiano bitterly complained about the minimal amount of information provided by modern soccer tables. Here are the first few lines of the current table of the Spanish soccer league:
Team M Pts GD ---------------------------------- 1. Villarreal 7 16 +7 2. Real Madrid 7 15 +13 3. Celta de Vigo 7 15 +8
Clearly the column M contains the number of matches played so far, the column Pts contains the number of points reached so far, and the column GD contains the current goal difference.
But what Cristiano really wants to know is the number W of won, the number L of lost, and the number D of drawn matches. And (according to Cristiano) there is no way of deducing these numbers from the information provided in the table.
Gareth Bale (who is mathematically gifted) observed that for Villarreal the numbers actually can be deduced: W=5, L=1, and D=1. On the other hand, for Celta there exist two different possible number triples.
Question: From which combinations of two non-negative integers M and Pts can one uniquely determine the three numbers W, L and D?
Note: For a win/loss/draw a team respectively scores 3/0/1 points.