### Heads, Tails And Beans |S|=2

Before we can start to solve some counting problems we need to know a little of combinatorics’ notation. Luckily, a few simple rules should get us started. Don’t worry if it doesn’t make sense, that [more…]

Before we can start to solve some counting problems we need to know a little of combinatorics’ notation. Luckily, a few simple rules should get us started. Don’t worry if it doesn’t make sense, that [more…]

Mathematics is not everyone’s cup of tea – fair enough. The Monday morning ‘double maffs’ articles by our resident mathematician, OldTrout, can present some GP’ers with a feeling of bewilderment. Myself included. I’m no mathematician. [more…]

A proof of Fermat’s Little Theorem using necklaces. , where is prime and is any integer with gcd. Multiply both sides of the congruence by : Which gives : Subtract from both sides : [more…]

When you do mathematics you spend much of your time being confused. We can go further with our counting and count the number of necklaces and bracelets with a particular colouring. When we counted the [more…]

A Cyclic group is a group that can be generated by a single element . The generator is denoted by and satisfies : , where is the identity element. A Cyclic group, , is the [more…]

“Rise above oneself and grasp the world” These are awarded every four years for advancement in the field of mathematics. There is an age limit of 40 on the recipients. It is a recognition [more…]

Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all . These numbers are called the totatives of . [more…]

The triangle numbers are equal to the sum of the natural numbers from to . The sequence begins : So the sum to the tenth natural number is : The square numbers are equal to [more…]

We wish to arrange the natural numbers such that adjacent pairs of numbers sum to a square number. Why can we find a Hamiltonian path for some numbers and not others? For a Hamiltonian path, [more…]

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