Friday 6 November. Think first, out loud. Take a hint only when stuck, then open the worked approach a step at a time.
Computer Science
Paths across a grid
On a 4 by 4 grid of squares, you walk along the lines from the bottom-left corner to the top-right corner, moving only right or up. How many different routes are there?
Hint 1How many moves does every route take, and how many of them are to the right?
Hint 2A route is fixed once you choose which moves are the right moves.
Every route has 8 moves: 4 right and 4 up.
A route is a choice of which 4 of the 8 moves go right.
That is 8 choose 4 = 8!/(4! 4!) = 70.
Check on a 1 by 1 grid: 2 choose 1 = 2 routes, which is right.
Where it lands: 70
The trap: Multiplying choices at each corner (2⁸): near the edges you only have one choice.
What a tutor might ask next: How many routes avoid the centre point of the grid?
Now do one out loud. In the interview you think aloud with a tutor. Try a Computer Science problem with hints, follow-ups and Mia's feedback on how you think.
Problems in your subject, answered out loud on the page. Take hints when stuck, answer the follow-ups, and see how your thinking comes across.
Oxbridge Interview Rehearsal: two subjects
£249 once. No VAT is charged.
Introductory price £249 until 31 December, then £399.
Rehearse every problem in two subjects you choose, with hints, follow-ups and Mia's marks, for 12 months.
All 8 problems in each of your two subjects, chosen after you pay
Hints when you are stuck, then the tutor's follow-up questions
Mia's marks on up to 60 attempts a day, within a fair-use allowance for each interview season: thinking aloud, using hints, checking, reasoning
Your next problem picked from your weakest skill
Your latest 300 attempts saved, with re-attempts side by side
Access for 12 months, until 6 November 2027. Choose your subjects after paying, on a free account. Full refund within 14 days, for any reason.
By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right. Your full refund within 14 days, for any reason, still applies.
Oxbridge Interview Rehearsal: all subjects
£349 once. No VAT is charged.
Introductory price £349 until 31 December, then £499.
Every problem in all seven subjects, for joint courses and for practising beyond your own subject.
All 56 problems: Maths, Computer Science, Engineering, Physics, Economics, Law and PPE
Hints when you are stuck, then the tutor's follow-up questions
Mia's marks on up to 60 attempts a day, within a fair-use allowance for each interview season: thinking aloud, using hints, checking, reasoning
Your next problem picked from your weakest skill
Your latest 300 attempts saved, with re-attempts side by side
Access for 12 months, until 6 November 2027. Use it on a free account. Full refund within 14 days, for any reason.
By paying you agree to our Terms and get access straight away, which ends your 14-day cancellation right. Your full refund within 14 days, for any reason, still applies.