# Difficulty – Medium

Medium difficulty brain teasers and puzzles

## Deducing Bicycle Spokes

A bicycle shop has some number of unusual bicycles. All their bikes are identical (there’s more than one bike), and each bike’s front and back wheels has at least one spoke each (each bike has more than one spoke). You don’t know how many bicycles are in the shop, but you know there are between 200 and 300 spokes in total.

If you knew the exact number of spokes, you would be able to figure out the number of bicycles.

You don’t know the exact number of spokes, but just knowing the fact that you would be able to figure it out with that information allows you to deduce the answer. How many bicycles and spokes are there?

## Card Pairing Game

You are playing a game with your friend using a standard deck of 52 playing cards. Each round, you flip over two cards:

• If both cards are black, you keep the cards and earn one point.
• If both cards are red, your friend keeps the cards and earns one point.
• If one card is red and one is black, the cards are set aside in a discard pile.

What is the probability that you end up with more points than your friend when all the cards in the deck have been used up?

## Nob’s Number Tree Puzzle

### Nob’s Number Tree

What number belongs in the “?” circle? Note that all numbers shown are correct, there are no typos or errors.

### Nob Yoshigahara’s Puzzles

Nob’s Number Tree is a well-known brainteaser by the Japanese puzzle guru Nobuyuki “Nob” Yoshigahara, who wrote many mathematical puzzle books and invented many puzzle toys. This cheeky number tree puzzle seems straightforward, but the straightforward solution falls apart when you arrive at the bottom.

Continue reading “Nob’s Number Tree Puzzle”

## Chance of Rain

You are driving to Seattle to meet some friends, and want to know whether you should bring an umbrella. You call up 3 of your friends who live there and independently ask them if it’s raining. Your friends like to mess with you, so each of them has a 1/3 chance of lying. If all 3 friends tell you it is raining, what is the probability it is actually raining there?

This question was asked in an actual Facebook data scientist/data analytics interview.

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