The Office Bet

The birthday problem as a story: a colleague bets that two of the 23 people in the room share a birthday.

Twenty-three people are in a meeting room. Dev puts fifty pounds on the table and bets that at least two of them share a birthday. Birthdays are uniform over 365 days and independent, and Dev wins if any two people match - not if someone matches him. The story asks whether you take the bet. You lock in a guess, then step through the answer and breakdown.

Why quant interviews test this

Interviewers are checking two habits - reaching for the complement, and knowing pair-counts scale quadratically - both of which transfer straight to collision estimates. The written solution is at /brain-teasers/birthday-problem/solution.

The The Office Bet guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

More Brain Teasers games

• Screwy Pirates - Five rational pirates vote on how to split 100 gold coins, and you work out the split by backward induction from a one-pirate crew up.
• Tiger and Sheep - A hundred rational tigers and one sheep on a magic island, where any tiger that eats becomes a sheep itself - solved by induction on parity.
• The Split Deal - The prisoner's dilemma played as a story: two thieves, separate rooms, and one offer each.
• Stag or Hare - The stag hunt as a story: two equilibria, and a choice that comes down to trust.
• One Offer, No Discussion - The ultimatum game as a story: one split of 100 pounds, one accept-or-reject, no negotiation.
• The Growing Pot - The centipede game as a story: a pot that doubles on every pass, and logic that says take it immediately.
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