One of the most magical aspects of mathematics is the ability for complex and intricate structures to emerge from the simplest of rules. Few mathematical objects are simpler to create – and few weave ...

The first four triangular numbers are 1, 3, 6 and 10, and the nth triangular number is given by the expression n(n+1)/2, so the 20th such number is 20 × 21 ÷ 2 = 210. ENIGMA is a triangular ...

Harry and Tom have each found a 4-digit perfect square, a 3-digit perfect cube and a 3-digit triangular number that use 10 different digits, but with no leading zero. A triangular number is one that ...