Interview Preparation

Cambridge interviews are academic conversations. Expect to explain your thinking and apply familiar ideas to unfamiliar problems. The format varies by College; follow your invitation and the official guidance.

Thinking out loud

State your assumptions, try small cases and explain what you are checking. Ask if a question is unclear. If you get stuck, say where and use any hint you are given.

You do not need to narrate every thought. Give the interviewer enough to follow your reasoning.

What a good answer sounds like

For a 2 × n strip tiled with 2 × 1 dominoes, small cases suggest a Fibonacci recurrence.

A vertical domino leaves a 2 × (n−1) strip. Otherwise, two horizontal dominoes fill the first two columns and leave a 2 × (n−2) strip. These cases give

$$T_n = T_{n-1} + T_{n-2}, \qquad T_1 = 1,\quad T_2 = 2.$$

Explain the cases, not just the pattern in the numbers.

Preparation

Reread your statement, practise explaining solutions aloud and ask someone to challenge your reasoning. Check any online interview equipment in advance.

The University preparation guide covers practical arrangements and practice interviews.

Afterwards

An interview can feel difficult without telling you how the application will turn out. Follow the official decision timeline rather than trying to infer a result from the conversation.