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My boss ask us a geometry question a few hours ago, but we can't find a solution at all..

We have a square prism that long edge is 12 cm and short (base) edges are 4 cm.

We have 2 points (A and B). And these are 0,5 cm away from the nearest egde (blue lines) and these points extensions divide two equal pieces (2 cm - 2 cm) their nearest edges.

The question is; Find a way to A to B smaller than 16cm..

The rule is; the way can't use inside of the prism, only can use surface of the prism.

First of all, for finding the shortest path, I tried to open the prism like;

Even with that way, |AB| will be more than 16 cm..

Is there any solution for <16 cm?

Note: I tagged the question with only geometry tag. So, please feel free to update it..

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1 Answer

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There are several different ways to unfold the net of the prism. Let me refer to the figure in the question.

Unfold the prism so that the left end is attached to the bottom face and the right end is attached to the top face. This gives a transverse distance of $2+4+2 = 8$ and a longitudinal distance of $0.5 + 12 + 0.5 = 13$. Pythagorean theorem then gives the straight-line distance as $\sqrt{233}\approx 15.264$.

Try this link for the picture.

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