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Saturday, July 26, 2008

Sneaking Spider

A rectangular room measures 7.5 meters in length and 3 meters in width. The room has a height of 3 meters. A spider sits 25 centimeters down from the ceiling at the middle of one of the short walls. A sleeping fly sits 25 centimeters up from the floor at the middle of the opposite wall. The spider wants to walk (i.e., move along the walls, floor, and ceiling only) to the fly to catch it.

The Question: How can the spider reach the fly, walking just 10 meters?

Answer: The shortest path between two points in a plane is a straight line. And since the spider moves via the sides of the room only, we can "unfold" the room to make it a plane, as follows:

The shortest path between the spider and the fly is the straight line AC. Since AB has a length of 1.5+3+1.5 = 6 meters and BC has a length of 0.25+7.5+0.25 = 8 meters, AC has a length of 10 meters.

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