In the spirit of some of my Raymond Smullyan favorites, here's a relatively hard puzzle from a Dennis Shasha collection of $1988$:
Eight kids and their guide are lost on a forest exactly one hour before night falls. They are on a glade from which four paths leave. The guide knows that one of the paths leads to the camp site in exactly $20$ minutes but doesn't know which one.
The guide thinks that the best solution to find the right path is send small groups of campers (where he could include himself) for $20$ minutes, then the groups turn back to the glade, share what they found with the others and finally, thanks to that information, they pick the right path and use the last $20$ minutes before night falls to reach the camp site.
It could be an easy foolproof plan, but the guide also knows that two of the eight kids (not which ones) like to tell lies one in a while.
How should the guide divide the groups to find the right path using this plan?
EXTENDING THE PROBLEM:
Since I didn't do my homework correctly (I didn't search properly for a duplicate problem - here), I decided to investigate a little variant so we don't waste this space on
Puzzling. Here it goes:
When the guide was ready to send the groups on their mission, he realized that the two possible liars were on the morning group. The group he was dealing with had three compulsive liars (they always lie) and two of them always walk together. Besides that, Martin, the youngest one, has to be part of a group of at least four people.
How should the guide divide the groups now?