Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

Weekly Challenge 12: Venn Diagram Fun

Stage: 5 Short Challenge Level:

Consider the Venn diagram for 3 sets $A$, $B$ and $C$ with each of the $7$ regions labelled as follows

The set-theoretic representation of these regions is

1. $C^c\cap B^c$

2. $A\cap B \cap C^c$

3. $A^c \cap C^c$

4. $A\cap C \cap B^c$

5. $A\cap B\cap C$

6. $B\cap C \cap A^c$

7. $A^c \cap B^c$

A four-region diagram can be constructed by overlapping four rectangles (blue, pink, yellow, red) as follows:

Note that there are $15$ distinct regions of the diagram, corresponding to $2^4-1$. If your diagram does not have exactly $15$ distinct regions then it is incorrect!