The Thue-Morse Sequence that shows over infinite tries the “fairest” way for two people to take turns when choosing things from a pool (i.e. drafting players for a kick-ball team). Matt Parker has a very entertaining YouTube video on the subject and John D. Cook has a clear example as well. Between two players the…
Math
Addition of Very Large Numbers
It’s not uncommon to get to a point in mathematics or programming that very large numbers must be dealt with. For the context of this post I will define a very large number (VLN) as any number that exceeds the maximum value of an unsigned 64-bit integer (aka ulong.MaxValue or 18,446,744,073,709,551,615). It’s surprisingly easy to…
Investigating Basic Combinatorics
In programming and in math we are often interested in how many possible combinations of objects exist. For example: how many 5-hand cards can be made from a 52-card deck? In mathematics these are referred to as combinatorics problems. Many basic combination problems can be evaluated with the formula: The formula is verbally stated as…
Finding Divisors And Prime Factors
Finding Divisors A divisor (D) of a number (N) is an integer that divides another integer with no remainder. In other words N mod D = 0. Sometimes, we are interested in finding all divisors of a number. If we are considering a programming solution to this problem, chances are we are dealing with very…
Prime Number Testing
A prime number (or a prime) is defined as a positive integer greater than 1 that has no positive divisors other than 1 and itself. If I wanted a programmatic test that a number is prime, my first instinct in C# would look something like this: static bool IsPrime(int number) { for(int i = 2;…