How many rational numbers are there between 0 and 1 for which q < p?

Find all rational numbers each of which is equal to its reciprocal.

A bus shuttles between two neigbouring towns every two hours. It starts from 8 AM in the morning and the last trip is at 6 PM. On one day the driver observed that the first trip had 30 passengers and each subsequent trip had one passenger less than the previous trip. How many passengers travelled on that day?

Find all integers such that is also an integer.

By inserting parenthesis (that is brackets), you can get several values for 2 × 3 + 4 × 5. (For example ((2 × 3) + 5 is one way of inserting parenthesis.) How many such values are there?