I'm Benjamin Curran. I'm a 14 year old puzzle lover and I come to you with this puzzle that I've made up myself.

Hopefully you won't find it tricky.

Two tourists have gotten themselves lost in the middle of nowhere! Luckily they remember a few things about their hike, but the rest is as hazy as a morning fog...

They remember turning around a few times during their stroll, but they don't remember the bearings of the turnings, although they remember the distances in which they travelled in, the fact that they always travelled in straight lines and knowing that not once did they ever split up.

The duo remember that they started setting up an overnight camp there and walked one kilometre from there, then they walked another kilometre in a different direction and finally, one kilometre in another direction.

Now here's the question:

What's the minimum possible distance the tourists could be from their camp?

This my first attempt at creating a riddle on Puzzling Stack Exchange. If you found it too easy that's okay. But if you enjoyed it that's also okay. Either way, just let me know.

  • 3
    $\begingroup$ Idea for a follow-up question: what's the average possible distance the tourists could be from their camp? $\endgroup$
    – Jerry Dean
    Commented Sep 18, 2021 at 6:09
  • $\begingroup$ @JerryDean I am afraid the "average" isn't uniquely defined and you might come up with very different results. Similar to the Bertrand Paradox. One way out would be to very specifically give the probability of the tourist's choices. $\endgroup$
    – Helena
    Commented Sep 18, 2021 at 8:14
  • 3
    $\begingroup$ @Helena I'm not sure there's really a simpler and more natural means of defining the sampling procedure other than "uniformly random angle of direction (0 to 2pi) at each of the three travels." After all, the three directions are the sole variables here. $\endgroup$
    – Feryll
    Commented Sep 18, 2021 at 9:07

1 Answer 1


The answer is...

0 km.
In other words, they're at the camp.

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  • $\begingroup$ Beat me to it lol $\endgroup$ Commented Sep 17, 2021 at 20:53
  • $\begingroup$ And it would also work on a sphere. $\endgroup$
    – daw
    Commented Sep 22, 2021 at 9:22
  • $\begingroup$ @daw That depends on your definition of a straight line - a sphere's surface is curved, after all. $\endgroup$
    – A username
    Commented Sep 22, 2021 at 9:30

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