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Two Slimy Slithering Snails

In a garden, two snails are hurrying along on their daily slither on a cylindrical column 6 feet around. Samuel was 2 feet up from the groud at the moment when Simona, on exactly the opposite side, was 6 feet up from the ground. Just then some molluskan 6th-sense made each aware of the other's proximity. Spring was in the air, and even snails have their special moments.

"Which way will he travel?" wondered Simona, halting in her slimy slither.

It was a long wait, but Samuel did not disappoint her. How far did Samuel travel to reach Simona by the shortest route?


Source: Adapted from J. Hunter's Fun With Figures, 1956

Hint: Roll and tape a sheet of paper together to represent the cylinder...then locate the positions of the two snails.

Can you draw a "straight line" between the two...knowing such is the shortest route?


Solution Commentary: To draw the line, cut the cylinder vertically through Simona's position and unwrap it. Draw a line between the two positions...do you see a right triangle forming, with sides 3 feet (i.e. half circumference) and 4 feet (i.e. vertical distance between their positions)...meaning Samuel's route is how many feet long?