I’m thinking about the following questions. They are to be completed using pencil and paper (or marker & whiteboard) only (and for questions 1 and 2, I’d accept the method and not worry about the actual calculated answer). At the moment, only one of them is a question I’ve actually given at interview. And I only use these questions for new graduates, as a way of gauging mental horsepower. If I’m interviewing someone with a few titles under their belt, for the best use of time I usually hit other areas.

Question 1. What is the sum of the multiples of 3 less than 1000? What is the sum of multiples of 3 or 5 less than 1000? [This is Project Euler problem 1]

Question 2. What is the smallest integer that is evenly divisible by the numbers 1 through 20? [This is Project Euler problem 5]

Question 3. How many trailing zeroes are there in the (decimal!) number 100 factorial when it’s fully written out?