## General puzzles

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It travels with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less or the same if, throughout both flights, at the same engine speed, a constant wind blows from A to B?

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You are given two cords that both burn exactly one hour, not necessarily with constant speed. How should you light the cords in order to determine a time interval of exactly 15 minutes? Extra question: how to light just one cord and measure 15 minutes?

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Solution
Source: Quant Interview
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There are two beakers, one containing water, the other wine (equal volumes). A certain amount of water is transferred to the wine, then the same amount of the mixture is transferred back to the water. Is there now more water in the wine than there is wine in the water?

Solution
Source: Common
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Light bulbs are numbered 1 to 100, and kept off initially. First person comes and toggles all the bulbs which are multiple of 1, i.e. he switches all bulbs to on. Second person toggles all multiples of 2, i.e he turns of even bulbs. Third person comes and toggles all multiples of 3. This process continues till 100 persons pass. After this, how many bulbs are ON?

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Without explicitly calculating, find out which is bigger: e^Pi or Pi^e?

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