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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.

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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}.

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Root to Poly

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

Alternating Sum

Stage: 4 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection

Given that the number 2008 is the correct answer to the calculation:
$$1-2+3-4+5-6+...+(n-2)-(n-1)+n$$

What is $n$?




 

This problem is taken from the UKMT Mathematical Challenges.