Showing what's behind the curtain

In the game, Monopoly, find the three most popular squares when using two 4-sided dice.

Investigating numbers that can be expressed as the sum of a prime square, cube, and fourth power.

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

Find the continued fractions for N ≤ 10000 have an odd period.

Investigate the Diophantine equation *x*^{2} − D*y*^{2} = 1.

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

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

Listing reduced proper fractions in ascending order of size.

Find the sum of the only set of six 4-digit figurate numbers with a cyclic property.

Exploring the shortest path from one corner of a cuboid to another.