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Weekly Challenge 43: A Close Match

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

Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

Weekly Challenge 28: the Right Volume

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

Weekly Challenge 22: Combinations of Two

Stage: 4 and 5 Short Challenge Level:

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.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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