Friday Puzzler: The solution

By Morwenna Evans Tuesday, May 27, 2014

Question

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Last week we asked you this tricky puzzle:

A revolving door includes three wings which rotate within a circular-shaped space. The door makes 4 complete rotations in a minute. There is room for a maximum of two people in each of the three door sectors. What is the maximum number of people that can enter the building through the door in 30 minutes?

Solution

Here is the long awaited solution to our Friday puzzler. Did you get the answer?

You may think this question may be more complicated than it actually is. Every minute it will rotate completely 4 times, meaning each section will be able to get 2 people into the doors and out of the doors through each sector every 15 seconds.

This is equivalent to 8 people in the building each minute through each sector and therefore 24 people through the doors every minute. Over the course of 30 minutes this amounts to 24x30 people which is 720.

Note that the question doesn’t ask how many people can enter or leave the building in 30 minutes; if this was the case the answer would require some logical thinking because initial thoughts are that it would be double the previous answer which would be 1440.

In actual fact this isn’t the case because there is only two ways to get into the revolving doors but three sections in the final rotation of the hour two people could get into one of the sections but not out. This means the actual answer to the harder question is 1438.

Let us know if you got it right!