A circle has radius 4 and perpendicular diameters `bar (AC)` and `bar (BD)`. Find the area of the shaded region.

Point `M` is the midpoint of `OA`, where `O` is the origin and `A(2, 5)`. Point `P (p, q)` is in the first quadrant and on the perpendicular bisector of `OA`. If `PM = AM`, find `p + q`.

Seven years ago was a fascinating year!

Find the sum of the prime factors (with repeats if they occur) of 2018.

Now find the sum of the prime factors of your answer.

Continue this process until your number remains unchanged.

What is that number?

A small country has exactly 15 cities, with no 3 cities on the same straight line. Straight roads joining each pair of cities are constructed. Find the number of roads.

The first term of an arithmetic sequence is 1 and the fourth term is 13. Find the tenth term.

Suppose `F(n)` represents the number of positive factors of the integer `n`. For example, `F(8) = 4`, since the factors of `8` are `1, 2, 4,` and `8`. Find `F(168)`.

Consider the following rule to determine the terms of a sequence:

1. The first term is 20.

2. If a term, `x`, is even, then the next term is `1/2x`.

3. If a term, `x`, is odd, then the next term is `3x + 1`.

Find the value of the 900 ^th term.

Let `X` be a 2-digit number and let `Y` be the number with the digits reversed. Find the 2-digit number that satisfies `3X − 4Y = 8`.

Evaluate `(−1)^(1!) + (−1)^(2!) + (−1)^(3!) + ⋯ + (−1)^(100!)`.

Note: `7!` (called seven factorial) is equivalent to `7xx6xx5xx4xx3xx2xx1`, similarly `4! =4xx3xx2xx1`.

A Mersenne prime number is one of the form `m=2^p − 1` where `m` is prime. The number `2^44497 − 1` is a Mersenne Prime. What is its units digit?

Alysha spends five weeks training for a distance race. After keeping track of the number of hours for the five weeks, Alysha notices the following:
a. The first week she trained 2 more hours than the average for all five weeks.
b. On the second week, she trained for 36 hours.
c. On the third week, she trained 7 more hours than the average of the first two weeks.
d. On the fourth week, she trained 8 hours less than the average of weeks two and three.
e. On the fifth week, she trained 2 hours less than the fourth week.
How many hours did Alysha train for in total over the five weeks?