You may also like

A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

Prime Counter

A short challenge concerning prime numbers.

The Right Volume

Can you rotate a curve to make a volume of 1?

Combinations of Two

Age 16 to 18 Short
Challenge Level

pascal triangle
Can you use this diagram to prove that the number of different pairs of objects which can be chosen from six objects, $^6C_2$, is $$1 + 2 + 3 + 4 + 5?$$
Generalise this to show that the number of ways of choosing pairs from $n$ objects is
 $$^nC_2 = 1 + 2 + ...+ (n-1) = \frac{1}{2}n (n - 1).$$ 
Did you know ... ?
The sum of the first $n$ whole numbers is called a triangle number because this sum can be represented geometrically by a triangular array of dots. The sum is easily found by working out the number of dots in the parallelogram formed by putting two triangular arrays side by side.