Oxford Mathematics and Computer Science interview

The Oxford Mathematics and Computer Science interview is academic and run like a short tutorial, and candidates usually have separate maths and computer science interviews. You talk through unfamiliar maths problems, and logic or algorithm puzzles with little or no computing in them, while tutors watch how you break a problem into small cases, take hints and justify a general answer. Shortlisted candidates generally have two interviews at their first college and at least one at a second, randomly assigned college, on Microsoft Teams: about 25 minutes for maths and 30 for computer science. For 2027 entry most run from 14 to 17 December 2026.

Key facts

What happens in the interview

Joint-degree candidates typically have separate maths and computer science interviews, though some colleges use one interview with tutors from both subjects.

• Maths interviews: an unfamiliar problem, a point of technique, a curve sketch or a new definition to explore.
• Computer science interviews: mostly mathematical puzzles and algorithmic problems (strategy games, counting, searching, invariants), often with "apparently no computing content at all". A computer science interview may open with a quick question about your motivation or personal statement.

Tutors run it like a tutorial:

• They shrink the problem, offering "an easier problem to start with".
• They suggest a first step, then ask what's left.
• They generalise (change 10 to 11, then to n) and ask you to justify the answer.
• They give hints freely.
• They switch to a new question to see a different kind of thinking.

Tutors would rather you asked a question than sat in silence feeling stuck. Slips don't matter much. Finishing a problem is rare, and getting through a significant part of it is a good performance.

You'll write on a shared Miro whiteboard, and questions may be shown on screen as a PDF. Have a touchscreen of at least 8 inches and a basic stylus, plus paper and pens, and leave earlier working visible rather than rubbing it out.

What tutors look for

The selection criteria for Mathematics and Computer Science:

• Mathematical ability: accurate, fluent school maths used as a tool, in both the maths and the computer science interviews.
• Absorbing and using new ideas: taking a hint, a new definition or the rules of a game, and applying it correctly and systematically.
• Thinking independently: breaking a problem into smaller cases, spotting a pattern or invariant, conjecturing and justifying it.
• Perseverance and enthusiasm: staying with hard problems, with enthusiasm for both maths and computing.
• Explaining your thinking: thinking aloud and giving a clear justification.

Tutors also look for curiosity about computing.

How the interview is marked

Oxford doesn't publish a marking scale for Mathematics and Computer Science interviews. The Mathematics department's admissions report says interviews for joint courses, Mathematics and Computer Science included, are graded from 1 to 9 against agreed descriptors. The descriptors, and any grade that leads to an offer, aren't public.

The grades are shared across colleges with your admissions test score and UCAS form, so no single interview decides the outcome. It's very common not to reach a complete solution, and getting through a significant part of a problem is a good performance.

Example questions

These are questions Oxford has published, in the form Toby asks them: one from a maths interview and two from computer science. Tutors set their own questions, so yours will differ.

Sliding ladder's middle rung

Published by Oxford: sample interview questions

A ladder leans against a vertical wall, with its feet on the ground. Its middle rung is painted a different colour, so we can see it from the side. As the ladder slides down to the floor, always touching both the wall and the ground, what shape does that middle rung trace out? Sketching a few positions might help.

• Why tutors ask it: it tests whether you can turn a physical picture into coordinates, check guesses against special cases, and notice when a model breaks down.
• A hint a tutor might give: "Try some special positions first. Where is the middle rung when the ladder is upright, when it's flat, and at 45 degrees?"
• A strong answer tests special positions before committing to a guess, then sets up coordinates with the corner at the origin and checks the endpoints of the shape it finds.
• A common slip is guessing a straight line.

Monkey beans

Published by Oxford Computer Science: sample interview problems

An urn contains 23 white beans and 34 black beans. A monkey takes out two beans; if they are the same, he puts a black bean into the urn, and if they are different, he puts in a white bean from a large heap he has next to him. The monkey repeats this procedure until there is only one bean left. What colour is it?

• Why tutors ask it: it shows whether you look for a quantity that never changes instead of simulating, the kind of invariant used to reason about programs.
• A hint a tutor might give: "Try tiny urns: one white and one black, then two whites and one black. What is left each time?"
• A strong answer looks for something that stays fixed instead of trying to follow 56 draws, checks each of the three kinds of draw in turn, and explains why the order of the draws doesn't matter.
• A common slip is arguing from probability, or from there being more black beans.

Missing numbers

Published by Oxford Computer Science: sample interview problems

Imagine you are given a list of slightly less than 1,000,000 numbers, all different, and each between 0 and 999,999 inclusive. How could you find (in a reasonable time) a number between 0 and 999,999 that is not on the list?

• Why tutors ask it: it shows whether you can design and compare methods for a large search, describe them precisely enough to carry out, and trade memory against time.
• A hint a tutor might give: "How do you know there is a missing number at all?"
• A strong answer first explains why a missing number must exist, then describes each method precisely enough to carry out and compares them by roughly counting their steps and the memory they need.
• A common slip is answering "the largest plus one", which fails if 999,999 is on the list.

Practise with Toby

Toby is an AI interviewer that runs practice interviews by voice. The Oxford Mathematics and Computer Science interview is built from Oxford's own guidance and follows the real format:

• First college: maths. A 25-minute interview with maths tutors: an unfamiliar problem, a point of technique, a curve sketch or a new definition to explore.
• First college: computer science. A 30-minute interview with computer science tutors: a logic puzzle or algorithmic problem (strategy, counting, searching), broken into small cases and then generalised.
• Second college. One interview at a randomly assigned second college, in either subject or with tutors from both, on a fresh problem.

It draws on 46 problems, each with hints and follow-ups. Nineteen are published questions from Oxford and Cambridge sources, and the rest were written to the same style and level, with every result independently re-derived. No programming is needed: as in the real interviews, the computer science problems are puzzles you reason through aloud.

Toby puts the problem on screen, gives you time to think and asks you to talk it through. He gives a hint only when you're stuck, asks you to justify your answer, and generalises the problem once you've solved a small case. Like a real tutor, he doesn't praise every answer.

You can add your personal statement so Toby can ask about it, and choose a 10, 20 or 30-minute interview. Your prep page has the format, the selection criteria and practice problems with hints and worked solutions. Afterwards, your debrief gives you a practice mark out of 10 (6 is acceptable, 7 good, 8 strong), a score against each criterion, notes on every question and the full transcript. A practice mark is a guide, not a prediction.

Frequently asked questions

Sources

Last checked October 2026.

• University of Oxford: Interviews
• University of Oxford: Sample interview questions
• Oxford Computer Science: How to apply
• Oxford Computer Science: What tutors look for
• Oxford Computer Science: Sample interview problems
• Oxford Computer Science: Admissions feedback 2025-26
• Oxford Mathematics: Mathematics and Computer Science
• Oxford Mathematics: Admissions feedback 2025
• Oxford Maths/CS Interview Questions (an Oxford tutor's page on the Computer Science department's website)

Related interviews

• Oxford Computer Science interview
• Oxford Mathematics interview
• Cambridge Computer Science interview

All Oxford and Cambridge interviews·University admissions

Toby is independent and isn't affiliated with or endorsed by the University of Oxford or the University of Cambridge.