### Football Board

**Source:**The Hidden Mathematics of Sport

**Problems:**

Football tables have been the basis of many a brainteaser over the years. These two puzzles ask you to work out what the scores were in all matches played so far this season.

Puzzle 1: Each team played the others once, what were the scores in each match (2 points for a win, 1 for a draw)?

**Played**

**Goals for**

**Goals against**

**Points**

**United**2103

**City**2212

**Albion**2021

Puzzle 2: The league table below got smudged in the rain, and is only partly legible. Eventually each team will play the others once, but the tournament isn't over yet. Can you find all the results?

**Played**

**Won**

**Lost**

**Drawn**

**Goals for**

**Goals against**

**Points**

**Athletic**32**44*

**Rovers***1*030*

**Town*****011*

**Wanderers*********

Update (27 Aug 2011):

Solution posted by Gautam Kamath (EE, Senior Undergraduate, IIT Bombay) in comments!