Continued Fractions
A continued fraction is a way to represent any real number as a sequence of integers by writing down the integer part of the real number and taking the reciprocal of the remaining part at each iteration.
Perfect Numbers
A perfect number is a natural number that is equal to the sum of all of its proper divisors (divisors that are less than the number itself). For example, 6 is the smallest perfect number because its proper divisors, 1, 2, and 3, add up to exactly 6.
Splitting LCMs (reworded)
Consider all pairs of natural numbers that add to 9, which pair has the largest possible Least Common Multiple?
Triangular and Trapezoidal Numbers
Triangular numbers and trapezoidal numbers are both natural numbers that can be expressed as the sum of more than one consecutive natural numbers.
Sum of Squares
Some numbers can be expressed as the sum of two perfect squares...
Sliding Puzzles
Sliding numbered blocks in a square grid to put them back in numerical order.
Colour Sorting Game
Constructing an unsolvable setup in a colour sorting game.
Connected Lights
Lights connected in a string or a loop, each attached to a switch that will change the state of the light itself and its neighbours when pressed.
Connecting Letters
Connecting letters on the left to their matching letters on the right without crossing any lines.
Seven
The card game Seven is one where players take turn extending the numerical sequences of cards in their respective suits.