# Sunday Times Teaser 2721 – Milliner’s Hat-Trick

*by Nick MacKinnon*

Four groups of four teams each play in a football tournament in which teams within a group play each other once. So far each team has played two matches and the distribution of points within each group is different. Also two teams in each group are level on points and have their positions set by their goals scored.

Nine players have each scored 1 goal, Milliner has scored 4 (including a hat trick) and Orlando has scored 2, although his team is not top of its group.

What are the results of the games played by Milliner’s and Orlando’s teams?

One Comment
Leave one →

This one is a very laborious programming exercise, one that is more easily done in stages. But here is a ‘more or less. complete solution. It does rely on an earlier and simpler partial solution that I used to determine that a minimum of 14 goals are needed when the teams in each group score the minimum number of goals needed to achieve a league position (i.e. all matches are 0-0 draws or 1-0 wins (or losses) except when teams are level on points when two goals are allowed). This hence leaves only one goal free to make a hat-trick by adding a goal to one of the 2 goal scores.