Quant-style brainteasers

Ten minutes into a quant phone screen, the interviewer drops the resume questions: "Two desks each make ten independent trades, and each trade wins with probability one half. What's the chance the first desk ends with more winners?" Then they wait. They are not checking whether you have seen the puzzle before. They are listening to how you start, whether you check your answer, and what you do with a hint. After this lesson you will have a short list of moves that open most of these puzzles, four original puzzles worked with them, and a way of talking through one that lets the interviewer follow your reasoning.

What the interviewer is listening for

A brainteaser is a small sample of how you think when nobody has handed you a method. The answer matters, but most of the score comes from the path:

• You pin the setup. Are the trades independent? Does a tie count as "more"? When the assumption changes the answer, as a tie does here, ask. When it is only a convention, state it and move on. If you have seen the puzzle before, say so.

• You bound it before you solve it. A rough range in the first minute shows you know what a sane answer looks like, and it gives you a check later.

• You talk while you work. Silence followed by a number tells them nothing. A wrong turn they can hear is a wrong turn they can steer.

• You check the result with a small case, a bound or a second method.

• You use hints. A hint is the interviewer helping. Drop the dead end and follow it.