Digit Sum Divisors
Consider a natural number N and the sum of its digits S. Let’s call a divisor of S a Digit Sum Divisor of N.
Water Jugs
Consider this family of popular puzzles: You have two empty water jugs with no markings. One holds exactly 8 liters of water when full, and the other holds 3 liters. You also have a full tub with an endless supply of water and another large unmarked empty jug of unknown volume. The goal is to measure out a given volume of water to put into the large jug using the other two jugs.
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.