# Maths item of the month

### March 2015

4 points, 2 lengths

In how many ways can you arrange 4 distinct points in the plane so there are exactly two different distances amongst the 6 pairs?

e.g. if the four points are at the corners of a square then the four sides are the same length and the two diagonals are the same length.

### February 2015

1, 2, 3, 4

Find two quadratic functions f(*x*), g(*x*) so the equation f(g(*x*)) = 0 has the four roots *x* = 1, 2, 3, 4.

Is it possible to find three quadratic functions f(*x*), g(*x*), h(*x*) so the equation f(g(h(*x*))) = 0 has the eight roots *x* = 1, 2, 3, 4, 5, 6, 7, 8?

### January 2015

Happy 2015: A Triple of Triples

2015 is the product of 3 distinct primes: 5×13×31

2014 and 2013 are also the product 3 distinct primes.

Can you find a smaller triple (*n*, *n*+1, *n*+2) where *n*, *n*+1 and *n*+2 are all the product of 3 distinct primes?

Are there any quadruples (*n*, *n*+1, *n*+2, *n*+3) where *n*, *n*+1, *n*+2 and *n*+3 are all the product of 3 distinct primes?