The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.
The 80 spokes of The London Eye are made from 4 miles of cable. What is the approximate circumference of the wheel?
Take four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. Does this always work? Can you prove or disprove this conjecture?
