Category Archives: puzzles

Birthday pairings

Here’s two classic birthday puzzles: How many people do you need in a room to have a better than 50% chance of finding at least one shared birthday among them? How many people do you need in a room with … Continue reading

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A perfect hand, with some combinatorial tricks

Question: You deal the first 13 cards from a well shuffled, 52-card deck. What are the chances the 13 cards you deal are of the same suit? There’s a couple of ways to do this – both incorporate useful techniques … Continue reading

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Puzzle – A safe place to drop an egg

This is a problem where it’s fairly easy to find the solution via trial and error, but not so easy to generalize. Question Let’s say you need to find out the highest floor in a 100 story building from which … Continue reading

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Alternating coin toss – redux

I want to revisit a probability puzzle from a previous post: see Alternating coin toss game. You play a game where you alternate tossing a coin with a friend, and the first person to toss heads wins. But let’s make … Continue reading

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Puzzle – Take your seats

Another problem that has an immediate intuitive answer, but can be tricky if you don’t have that insight. Question Let’s say there are 100 people, including you, waiting to board a fully booked flight, each with an assigned seat. The … Continue reading

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Puzzle – Leaning Tower of Pisa

Let’s say you drop a ball from the Leaning Tower of Pisa, which is 179 ft high, and it bounces back 10% of the dropped height – 17.9 ft. Then on the second bounce it bounces up 10% again – … Continue reading

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Puzzle – Break a stick to get a triangle

I read somewhere this is a Google interview question: Let’s say you drop a stick, breaking it randomly in 2 places, leaving you with 3 smaller sticks.   What’s the probability you can make a triangle out of the 3 resulting … Continue reading

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Puzzle – 4 Bugs chasing each other

The answer to this problem is either really obvious, or it’s not. Say there are four bugs standing at the corners of an imaginary 1m * 1m square.  Each of the bugs is facing the bug that is on the … Continue reading

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Puzzle – Liars and Truthtellers

This is another probability question that seems straightforward but can be deceptive… You’re an FBI agent and have been monitoring a large gang, and you know that 1/4 of its members always tell the truth, the rest always lie.  Then … Continue reading

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Puzzle – shortest road system

Let’s say you’re contracted to build roads to connect four towns that are at the corners of an imaginary square with sides 1 mile. What’s the shortest length of road system you can build so that every town can get … Continue reading

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