With the Cricket World Cup well under way, we have a puzzle based on the competition. But don't worry if you know little or nothing about cricket; you don't really need to know anything about cricket per se, and all will be explained.
There are ten teams in the competition, and in the group stage every team plays the other nine teams once. So at the end of the group stage all the teams will have played nine matches.
For each win the team gets two points, for a loss the team gets zero points, and for a tie (or no result - don't worry about it) the team gets one point. If two teams are level on points the team with the best net run rate (again don't worry about it) is placed higher.
The top four teams in the table at the end of the group stage qualify for the semifinals.
The questions are:
- What is the highest number of points that a team can get and not qualify for the semifinals?
- What is the lowest number of points that a team can get and still qualify for the semifinals?
In the first question we are looking at a situation where the top five teams are level on points, and with the highest number of points they can get. This means that the top five teams must win all their matches against the bottom five teams. So they all have five wins, which gives ten points.
In addition, all of the top five teams have four games against the other teams in the top five. The simplest way to imagine this is if all these games are tied, and each team gains four points for four ties.
These four points added to the ten points from the five wins above gives 14 points. So a team could fail to qualify with 14 points.
In the second question we are looking at a situation where the bottom seven teams are level on points, and with the lowest number of points they can get. This means that the top three teams must win all their matches against the bottom seven teams. So the bottom seven all have three losses, which gives zero points.
In addition, all of the bottom seven teams have six games against the other teams in the bottom seven. The simplest way to imagine this is if all these games are tied, and each team gains six points for six ties.
So a team could qualify with six points.