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Photo: Michael Niestedt / DER SPIEGEL
The two hikers could of course have known beforehand that you need a lot of water to cross the desert.
Nevertheless, everyone only has one water bottle with them, which always has to be refilled as soon as the opportunity arises.
The goal on this day is a desert camp that is a long way away from a narrow river - the only water source far and wide.
Because there is no fresh water in the camp itself, the hikers decide to make a detour to the river beforehand.
They want to drink plenty and fill up their bottles there.
The course of the river follows a straight line across the desert - see sketch.
Which route should the hikers choose so that the total route from the current location to the river and from there to the camp is as short as possible?
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Obviously, different ways are possible.
The two hikers have already measured the distances between the location, river and camp on a map and are starting to calculate wildly.
What's the shortest way?
Please scroll down to find the solution!
Photo: Michael Niestedt / DER SPIEGEL
solution
A simple trick solves all the difficulties the task poses.
Perhaps you have tried to calculate the length of the path with the Pythagorean Theorem?
That was my first idea too, but it leads to complicated equations.
It is much easier, without arithmetic: just mirror the point on the right, which stands for the camp, up the river and then see what happens - see the following graphic.
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We immediately see: The path from the river to the point on the lower right is just as long as from the river to the mirrored point on the upper right.
This follows automatically from the fact that the point was mirrored on the river.
Now we can formulate our task differently: Find the shortest path from the point at the bottom left, the location of the hikers, to the mirrored point on the other side of the river - i.e. to the point at the top right.
And what is the shortest connection between two points in the plane?
A straight.
So we draw these in and we're done.
If this riddle sounds familiar to you - it appears in my 2012 book "The more holes, the less cheese - mathematics amazingly easy".
If you missed a puzzle from the past few weeks, here are the ten most recent episodes:
The impossible cube
Which word did Stefan choose?
Cut a square into four triangles
An amazing card trick
The sawed-up horseshoe
The strange clock
Lies, Truths, and a Virus
How long does the chain have to be?
Total known, numbers sought
The bar castling
Icon: The mirror
