Challenges cover a variety of topics
You will need all your skills in graph theory, and pathmaking, algebra and combinatorics to solve today’s challenge. Good luck!
This captivating circle has been divided in to many sections. By combining these sections, you can make many different composite shapes. The challenge is to see how many shapes you can make. This includes the entire circle.
In this captivating circles challenge, you will need to use some algebra, some combinatorics, and some serious brainpower.
For our newest captivating circle, we are dealing with splitting oranges. The orange starts with N slices in a circle. It is then divided into 2 rings with A slices and B slices. In the diagram, N=9, A=3, and B=6. We then count one 3 and one 6. One of these rings is splitted to make 3 rings in all. We then count these rings. This continues until we can no longer split any rings as they all contain 1 slice. It happens that at the end, the number 1 is counted at least 3 more times than 2, which is counted at least 3 more times than 3, etcetera until the largest number counted. The challenge is this: what is the maximum value for N?
Today, we have a new captivating circle, and it is the first challenge to require the use of combinatorics. It also requires some trig and pathmaking.
Our second captivating circle is a circle with 7 points on its circumference. The points are equally spaced. Each point connects to 2 others through the circle and 2 others through a straight line. No points can connect to another through both a line and arc. The circle has circumference π. How many possible different sets of connections can be made? And of these, what is the highest possible distance that must be traversed to get between 2 points?