One interview puzzle a day. From the companies that set them.

Ann is in the users table. She isn't in the result. Why?

users: 1 Ann (sex NULL), 2 Steve (m), 3 Mary (f), 4 Brenda (f) friends: (1, 2) (1, 3) (2, 3)

SELECT users.name, COUNT(friends.user1) AS count
FROM users
LEFT JOIN friends
  ON users.id = friends.user1
  OR users.id = friends.user2
WHERE users.sex = 'f'
GROUP BY users.id, users.name;

Which rows come back, and what is each count?

You don't know how many $1 bills are in the jar. You don't need to.

A jar holds three $20 bills and an unknown number of $1 bills.

Yesterday Grandma added one more bill: a $1 or a $20, 50/50.

Today you draw one bill at random. It's a $20.

What's the chance yesterday's bill was a $20? Comment with the fraction and why.

The answer isn't 6.

Start at one corner of a cube and finish at the corner diagonally opposite.

Move only along the 12 edges, and never visit the same corner twice. Paths of any length count.

How many different paths are there? Comment with the number and how you counted.

Rewards program or a 3-month sale: which makes a retailer more money?

A retailer has 10 million customers. Each spends $100 a year, spread evenly over the year.

Option A, rewards program: 25% join, each pays a one-time $50 fee, members always get 20% off. Option B, seasonal sale: 20% off for 3 months a year, and in those months spending doubles before the discount.

Which brings in more revenue this year, and by how much? Comment with both totals.

Each robot can reach a free space on its own. Does that mean they can all park?

6 parking spaces in a row, numbered 1 to 6. Robots start in spaces 1, 2 and 6. They must finish in spaces 1, 5 and 6.

Each robot moves one space left or right, or stays put. Only one robot can finish in each space.

Possible or impossible? Comment with your answer and the catch.

How much does a water park make on its busiest Saturday? You get 7 numbers.

Estimate one peak Saturday: 4 slides, open 10am to 5pm, no downtime 100 riders per slide, per hour Each visitor rides 2 slides on average Tickets: $300 over age 12, $250 under 12, and 70% are over 12 80% buy food and drink at $50 50% buy merchandise at $20

How many visitors, how much from tickets, and how much in total? Comment with each step.

6 snowboards. 6 days. A random board each day. How many get used?

Rachel owns 6 snowboards. Each day for 6 days, a student picks one at random. The same board can be picked again. At the end she sharpens every board that got used.

On average, how many does she sharpen? Comment with the number and why.

Day 7 of 30, from Intercom's guide to RICE prioritisation, using its own example projects.

RICE = Reach × Impact × Confidence ÷ Effort. Reach is per quarter, effort is in person-months.

Project 1: 500 people a month reach this step and 30% pick the option. Impact 3, confidence 100%, effort 2 Project 2: reach 2,000 a quarter. Impact 1, confidence 80%, effort 4 Project 3: a one-time effect on 800 people this quarter. Impact 2, confidence 50%, effort 1

Which do you build first? Rank all three, with scores.

Day 6 of 30, from McKinsey's public practice case, Electro-Light.

You're launching an electrolyte sports drink in the US: 8,000 million gallons of sports drinks sell a year 5% of that is electrolyte drinks, your market Each 16 oz bottle is 1/8 of a gallon You make $0.10 a bottle ($2.00 price, $1.90 cost) The launch costs $40 million

What share of the electrolyte market do you need to break even? The real case is solved without a calculator.

Comment with the share and each step.

Day 5 of 30, a question Optiver says it has used in trading interviews.

Choose how many fair dice to roll. Roll them all at once. You win only if exactly one die shows a six.

How many dice give you the best chance? And what is that chance?

Comment with your number, the chance and why.

Day 4 of 30, from Jane Street's trading interview guide.

You roll two fair dice.

1. Before you know anything: what's the chance the two numbers multiply to 1? 2. Then I tell you the sum is 2. Now what's the chance they multiply to 1?

Give both chances. Did knowing the sum change the answer, and why?

Day 3 of 30, from Jane Street's trading interview guide.

Flip a fair coin until you get three heads in a row. A tail resets the streak.

On average, how many flips does it take, counting the final three?

Most people say 8. It isn't.

Comment with your number and why.

Day 2 of 30, adapted from Capital One's case interview practice guide, with prices in dollars.

A new magazine, per subscriber, per year: +$25 subscription, 50 issues +$50 from ads, $1 on every printed copy -$50 printing and delivery, $1 a copy And $1 million a year in fixed content costs.

1. How many subscribers do you need to break even? 2. Twist: every subscriber comes from direct mail. A letter costs $0.50 and 2% of people say yes. Now what?

Ignore renewals and every other cost. Comment with both answers and your working.

Day 1 of 30, from Jane Street's trading interview guide.

Roll a fair six-sided die. You win that many dollars.

Once you see it, you can keep it or re-roll once. If you re-roll, you have to take the second number.

Which first rolls do you keep? And on average, how much do you win if you play it right?

Comment with your rule and the math.