I saw this puzzle a while back in a children's puzzle book, but I'll try to make it as accurate as possible.

There is a small army of three ants walking down a very narrow road, so there is only room for them to walk single-file. They come across another small army heading the opposite direction. Neither army wants to fight (ants are peaceful, I think), but it seems as if they have no options. Fortunately, one clever ant spots a small clearing in the trees, that only one ant can fit into at a time. Can the armies pass each other without having to fight? If so, how do they do this?

I have made a very bad illustration of this so it will hopefully be easier to understand, but if you need clarification I can provide it. Only one ant can fit into the hole at a time, and the road is long enough for both armies to fit on one side of the hole. This is not a puzzle, so don't post any answers like "These ants aren't peaceful."


Edit: I actually included the picture this time.

  • $\begingroup$ Maybe you were thinking of this? smart-kit.com/s7284/frog-jumping-puzzle Here, only one ant can pass while there's on in the clearing. $\endgroup$ – TheRubberDuck Nov 14 '14 at 2:11
  • $\begingroup$ @EnvisionAndDevelop Yeah, that seems more like it. Quite a bit harder, isn't it? $\endgroup$ – mdc32 Nov 14 '14 at 2:45

The first ant of side A (call her "A0") goes into the clearing, and the other back off. While A0 is in the clearing the whole B army pass the clearing so A0 now can go away.


  • $\begingroup$ Uhh, yes. Now that I see how simple this solution really is I feel like there was more to the problem. Oh well, you got it right anyway. $\endgroup$ – mdc32 Nov 14 '14 at 1:15

Ant 1 of Army Alpha gets in the clearing, less call him A1. All soldiers of army Delta pass the clearing. A1 goes away
Ant 1 of Delta army gets into the clearing. lets call him D1. Soldiers of Delta and Alpha pass the clearing and go to Delta Army side, D1 goes away.
A2 gets in the clearing, all armies go to Alpha side. A2 goes away.
Same process with D2, A3 and D3.


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