OMK 2018

A cuboid has an integer volume. Three of the faces have different areas, namely $7, 27$ , and $L$ . What is the smallest possible integer value for $L$ ?

Given a regular polygon with $n$ sides. It is known that there are $1200$ ways to choose three of the vertices of the polygon such that they form the vertices of a right triangle. What is the value of $n$ ?

Determine the value of $(101 \times 99)$ - $(102 \times 98)$ + $(103 \times 97)$ - $(104 \times 96)$ + ... ... + $(149 \times 51)$ - $(150 \times 50)$ .