Computer Science interviews at Oxford and Cambridge are most likely to contain questions on relevant maths content, including probability and recursion. While improvising possible questions, I came up with this one. I think it’s a little too hard to get through in a successful interview.
Alice and Bob play a dice game. They take it in turns to roll a (fair, six-sided) die.
Alice’s first roll – no matter what Alice rolls, the game continues.
Bob’s first roll – if he rolls more than Alice’s most recent turn, he immediately wins, and the game ends.
Alice’s second roll – if she rolls more than Bob’s most recent turn, she wins.
The game continues until a player rolls more than the previous roll.
a) Describe how some typical games will play out.
b) Calculate the probability that Alice will win.
c) If you get to a solution (or not), how would you like to check it?
In an interview, it’s not necessarily expected that you’ll get to the answer. Your exploration of the idea, with directed guidance from a tutor, is more important.
Would you like to do some interview practice with me for Computer Science and Mathematics for Oxford, Cambridge and other university courses? The questions will be challenging, but not this difficult!