Mathematicians: how to apply

The timing of recruitment campaigns varies, but details are always published on this website once confirmed. Tailored application forms only become available during each campaign.

We advertise in the national press and on various Internet job boards. Vacancies are posted on the recruitment website, www.careersinbritishintelligence.co.uk, and you can apply online from there.

Please pay particular attention to the nationality rules, which require you, among other conditions, to be a British citizen. Candidates whose spouses or cohabitees are not British may be also ineligible for security clearance. Each case is considered on its merits, however, so check with us on this point as early as you can in your application.

Test

The recruitment selection process involves a test in Mathematics and Computer Algorithms. Examples of past questions are given below.

Mathematics

1. Find a 3 by 3 matrix A, whose 9 entries contain at least 5 different non zero integers, with the property that: A³-7A=6I

2. Alice and Bob play coin toss: Alice pays Bob £1 for each head and Bob pays Alice £1 for each tail they throw. They continue playing until one player loses (runs out of money). Initially Alice has £6 and Bob has £14.

1. Determine, with proof, the probability that Alice loses.
2. Determine the probability that Alice loses but also has at some time previously been within £1 of winning.

Computer Algorithms

3. A polygon is defined by a set of n vertices P₁=(x₁,y₁), P₂=(x₂,y₂), P₃=(x₃,y₃), …, P_n=(x_n,y_n), and you may assume that the line segments P₁P₂, P₂P₃, …, P_n-1P_n, P_nP₁, do not intersect, other than at the vertices P₁, P₂, …, P_n.

Describe an algorithm to test if the polygon P₁P₂ P₃ …P_n is convex, given as input the co-ordinates (x_i,y_i), for i= 1,2,…, n.

4. A message to be enciphered consists of a sequence of n pairs of decimal digits. Each pair (x₁, x₂) is enciphered by a single digit k of One Time Key to produce a cipher pair (z₁, z₂) such that z₁=x₁+k mod 10, z₂=x₂-k mod 10. The encipherment is repeated r times to produce a cipher text consisting of rn pairs of digits (r>1). On receipt the message is deciphered and the cipher is "destroyed" by cutting it up into its constituent pairs. A spy retrieves the pieces and counts them, obtaining the results given below. What is the value of r?

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