### Cosines Rule

Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.

### DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

### Root to Poly

Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.

# Weekly Problem 1 - 2008

##### Stage: 3 and 4 Challenge Level:

$n$ is clearly odd, so we can write the series as:
$1+(-2+3)+(-4+5)+...+(-(n-1)+n)$. So the sum is the same as $1+1+...+1=(n+1)/2$.

So $(n+1)=4016$, so $n=4015$

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem