Showing what's behind the curtain

Listing reduced proper fractions in ascending order of size.

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

Find the number of fractions that lie between 1/3 and 1/2 in a sorted set of reduced proper fractions.

Determine the number of factorial chains that contain exactly sixty non-repeating terms.

Count the different lengths of wire that can form a right angle triangle in only one way.

How many different ways can one hundred be written as a sum of at least two positive integers?

Find the first value which can be written as the sum of primes in over five thousand different ways.

Investigating the number of ways in which coins can be separated into piles.

By analysing a user’s login attempts, can you determine the secret numeric passcode?

Calculating the sum of the decimal digits of irrational square roots.