Free Interview Resources
Free practice questions, preparation advice, and expert insights for Computer Science interviews at Oxford.
Real Computer Science interview questions in the style Oxford asks. Try answering each one aloud before you reveal the hint.
Tidy boxes: you have 10 boxes, 100 blocks, and 10 colours; show that the blocks can be packed so that each box contains at most two colours.
Problem-Solving
Hint
Start with fewer boxes and use the average number of blocks per colour to eliminate one colour at a time.
Searching for the maximum: a function on [0,1] increases up to a single maximum m and then decreases; how would you approximate m if you can choose only 10 function values?
Problem-Solving
Hint
Think about interval reduction rather than trying to calculate the function explicitly.
Death by chocolate: you and an opponent take turns breaking off and eating pieces of a rectangular chocolate bar containing one poisoned square; after seeing the bar, should you go first or second, and what is your strategy?
Problem-Solving
Hint
Begin with a 1-row bar or with the poisoned square in a corner, then look for symmetry or a smaller losing position.
Lily-pad lunacy: a frog starts on pad 0 and wants to reach pad 10, jumping forward by either one or two pads each time. How many different ways can it get there?
Problem-Solving
Hint
Let F(n) be the number of ways to reach pad n and relate it to earlier pads.
Missing numbers: you are given slightly fewer than 1,000,000 different numbers, each between 0 and 999,999 inclusive. How could you find, in reasonable time, a number from the range that is missing?
Problem-Solving
Hint
Think about what information you need to store and what time and memory trade-offs are available.
Tutorial-style interviews with subject-specific problems, often involving unfamiliar material.
Oxford interviews typically take place at the college you applied to. You will usually have two or three interviews of around 20-30 minutes each, sometimes at different colleges if you are pooled. The atmosphere is meant to resemble a tutorial: the interviewer gives you a problem and watches how you reason through it.
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
Interview Invitation
Late Nov
Arrival to Interview
Early Dec
Technical Question
Mid Dec
Decision
Early Jan
Let n be a perfect square. Pick floor(n/2) natural numbers from 1 to n-1 so that none is a perfect square and no two chosen numbers add to n. For what values of n is this possible?
hardHint
Pair the numbers that add to n and ask which pairs are unavailable because they contain a square.
Find the smallest natural number ending in 6 such that moving the final 6 to the front gives a new number four times as large.
midHint
Work from the units digit and use ordinary long multiplication with carries.
For the same function, focus on Z(2). Can you find an upper bound?
midHint
Try comparing 1/k^2 with a telescoping expression or grouping terms by powers of 2.
Given the ten-digit number 7106419902, remove three digits to obtain the largest possible seven-digit number; then explain a general strategy for deleting k digits from an n-digit number.
midHint
For the first remaining digit, ask how far into the number you are allowed to look while still leaving enough digits.
Draw all increasing trees with 4 vertices, then determine how many increasing trees there are on n vertices.
hardHint
Build an increasing tree on n+1 vertices by adding the new largest label to a tree on n vertices.
Minimise the expression below, where the positive real numbers a_1 to a_8 add up to 27.
hardHint
Try interpreting each square-root term as the length of a line segment, then ask when a broken path is shortest.
Monkey beans: an urn contains 23 white beans and 34 black beans; a monkey repeatedly removes two beans and replaces them according to the stated colour rule until one bean remains. What colour is the final bean?
entryHint
Look for an invariant: what changes, and what never changes, after each move?
Scribble: starting from PQ and using the stated rewriting rules on letters P, Q and R, decide whether QPR, PQQ, PQR and PR can be made, and then describe a procedure for deciding any word.
hardHint
Try small derivations, then search for a quantity modulo something that is preserved by every rule.
For the function below, find a lower bound valid for all s > 1 and explain why s = 1 is excluded.
midHint
Inspect the first term and then compare the s=1 case with a familiar divergent series.
Show geometrically why the inequality below holds.
midHint
Draw a unit circle sector and compare areas of the inner triangle, sector, and outer triangle.
For the minimisation problem above, can the values of a_i that minimise the expression be rational?
midHint
Once the straight-line condition is identified, check the proportionality constants explicitly.
Generalise the digit-moving puzzle: for a final digit d between 1 and 9, and a multiplier k, give a procedure to find the smallest number whose final digit moves to the front to give k times the original number. Is it always possible?
hardHint
Abstract the carry process from the concrete d=6, k=4 example and look for termination conditions.
For increasing trees on n vertices, give an algorithm to generate one uniformly at random.
hardHint
Use the recursive construction and make each valid parent choice with the right probability.
Extend Tidy boxes: if there are ten boxes but eleven colours, can the same two-colour-per-box guarantee still be achieved? What changes for twelve colours?
hardHint
Adapt the average argument, then construct or rule out a counterexample for twelve colours.
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Official demonstration of the style and structure of an Oxford Computer Science interview.
Course overview from Oxford tutors and students.
Helps applicants understand the department environment.
Useful only as supplementary practice after official materials.
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Further Reading
by Kevin Houston
Good for proof habits, mathematical language, and explaining reasoning clearly.
by Anany Levitin and Maria Levitin
Builds algorithmic thinking through puzzles close in spirit to interview discussion.
by T. W. Körner
Develops counting, estimation, and mathematical storytelling beyond the syllabus.
by Charles Petzold
Useful for connecting logical foundations to computing systems.
by A. K. Dewdney
Broadens subject knowledge across classic Computer Science ideas.
by University of Oxford Department of Computer Science
Primary source for authentic Oxford CS interview-style prompts.
by University of Oxford Department of Computer Science
Shows how a mathematical conversation may develop from an initial problem.
by UAT-UK
Official preparation hub for the required admissions test.
by University of Oxford Mathematical Institute
Oxford-specific guidance on TMUA preparation and specification.
by Varun Kanade
Named Oxford CS tutor source linking to past Maths/CS interview problems.