# IPL Quiz

Today, while having lunch in the office cafetaria, one of my friends popped up a question "What would be the minimum number of matches that a team has to win to ensure a place in semi-finals(top 4 teams in points-table make it to semi-finals) irrespective of the points table and net run-rate?" First, it appeared as a simple question. But the current format of the tournament is not symmetric, so we felt that it was not easy to compute this number. In the current league format, there are 10 teams, each team is playing 14 matches such that it is playing two matches each against 5 teams(both home and away), 1 match each against 2 teams(home) and 1 match each against 2 teams(away).

So, the first question is what would be the minimum number of matches that a team needs to win to ensure a place in semi-finals of IPL-4.

Then I came up with another question that what would be the minimum number of matches that gives a team a slim chance that it may still play in the semi-finals such that there exists a configuration of points table at end of group stage which allows this team to get through to the knockout stage.

Then we discussed, what if the conditions were symmetric like in the last edition of IPL when there were 8 teams and each team played 2 matches each against the remaining 7 teams. Both the questions we were discussing were a bit easier to solve in this case. What do you think is the answer?

For example, say if 4 teams were playing in a league such that each team played against each other i.e. there would be a total of 6 matches. Then, the minimum number of matches that a team must win to ensure its place in finals would be 3 i.e. win all it's matches. However, the minimum number of matches that a team must win to have a slim chance of making it to the finals is just 1.

So, what do you think would be the answer to these 2 questions in case of IPL-3 and IPL-4 and please give the reasoning behind your answers.

# Dividing into 4 identical shapes

I am going to describe here a logical puzzle which involves dividing  a given shape into 4 identical shapes.

Problem 1: Draw a square. Divide it into 4 identical squares. Remove the bottom left square and divide the resulting shape into 4 identical shapes.

Problem 2: Draw an equilateral triangle. Divide it into 4 identical shapes. Now, remove the bottom leftmost shape and divide the resulting shape into 4 identical shapes.