Sorry you're right. I thought about it, but then forgot it when I wrote the post!

And about This is what we must prove. It's not so evident. It is true, but how to show it? Suppose the first team won all his matches, so 14 matches. He got 28 points.

The first got 28 points, the last 7. How can you show that the 13 other teams cannot have different points between 7 and 28? It remains a range of 20 possible scores for 13 teams. Of course if you try you'll find out that it's impossible, but it's not rigorous.

There are $\displaystyle 210$ points to give. $\displaystyle 210-35=75$ points to give to 13 teams.

Say you give 8 points to a team, 9 to another, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. It makes 182 points. Added to the 35 given points, it make 217 which is not 210. So we see that the first team cannot have won all his games (it doesn't mean it has at least one draw). As the score got overpassed by 7 points, the problem is not finished and not evident. It's more complicated.

I repeat, from ,

**you must show **__why__ there's no way to distribute the points as it must be.

Have a nice day you too.