Hard puzzles




Hard Probability

An ant is standing on one corner of a cube & can only walk on the edges. The ant is drunk and from any corner, it moves randomly by choosing any edge! What is the expected number of edges the ant travels, to reach the opposite corner?

Hint
Solution
Source: Quant Interview
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Hard Probability

What is the expected distance of any point on Earth and the north pole? Take Earth radius 1.

Clarification: Shortest distance cuts through the sphere, instead of lying on surface.

Further thinking: Is this question same as choosing two random points on unit sphere and asking their expected distance?

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Answer
Solution
Source: Quant Interview
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Hard Probability

A stick is broken into 3 pieces, by randomly choosing two points along its unit length, and cutting it. What is the expected length of the middle part?

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Answer
Solution
Source: Quant Interview
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Hard Probability

There are n letters and n envelopes. Your servant puts the letters randomly in the envelopes so that each letter is in one envelope and all envelopes have exactly one letter. (Effectively a random permutation of n numbers chosen uniformly). Calculate the expected number of envelopes with correct letter inside them.

Hint
Solution
Source: CSEblog
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Hard Probability

A soda company is holding a contest where everyone who collects one each of N different coupons wins some prize. You get a coupon with each purchase of a soda, and each coupon is equally likely. What’s the expected number of soda bottles you have to buy in order to collect all the coupons?

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Solution
Source: Quant Interview
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