# Number Theory

Math puzzles and brain teasers involving the properties of integers

## 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?

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## Flipping Every N-th

There are 100 face-down cards. The first person that passes by flips over every card, the 2nd person that passes by flips over every 2nd card, and so forth – the n-th person that passes by flips over every n-th card. Before you know it, 100 people have passed by.

After all 100 people have passed by, which cards are face-up and which are face-down?

Fun fact, this was an actual brainteaser given to me in the first round interview for a hedge fund internship back in 2011.

Preparing for a brain teaser interview? Check out our ultimate guide to brain teaser interviews.

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