You are lost in the woods and the path you are following forks into two: a path to the left and one to the right. One path will lead you to safety while the other will cause you to be lost forever.
At the fork are two twin sisters who know which path is which. The sisters are identical in every way except one: one of the sisters always tells the truth while the other always lies.
You can ask only one question and you don’t know which sister is which. What can you say to them so you know which path to take?
Ask one of the sisters which path their sister would tell you to take.
Let’s say the left hand path is the correct one to follow. The sister that lies knows their truthful sister would tell you the left hand path, so as they always lie they will tell you the right hand path.
The honest sister knows their lying sister will tell you the right hand path and because they’re honest, they will tell you this. So you should follow the opposite path to that which you are told, regardless of which sister tells you.
I flop around on sticks and sometimes you cheer me as I do, I desperately need a white powder to do what needs to be done, and looking at me you might wonder why I look like I am about to go swimming. What am I?
I have a clock in my house, on the wall.
On a summer's day I forgot to wind it and it stopped. Then I went to visit a friend who had a watch that was always right on time. After I stayed for a bit, I went home, made a simple alteration and set the clock just right.
Now how did I do this when I had no watch on me to tell how long it took me to come back from my friend's place?
Before I left, I wound the wall clock. Upon my return, the amount of change that I could see in the clock is how long it took to go to my friends place and come back, adding to that the time I spent there, which I know because the clock at my friend's place is accurate.
Subtracting the time of the visit from the time I was absent from my house, and dividing by 2, I obtained the time it took me to return home. I added this time to what my friend watch showed when I left, and set the sum on my wall clock.
You have been given the task of transporting 3,000 apples 1,000 miles from Apple-York to Strawberry-Ville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Strawberry-Ville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Apple-York).
What is highest number of apples you can get to Strawberry-Ville?
How to solve:
You need to make 3 trips of 1,000 apples - 333 miles. You will be left with 2,001 apples and 667 miles to go.
Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Strawberry-ville.
This was Gollum's final riddle from The Hobbit:
"This thing all things devours;
Bird, beasts, trees, flowers;
Gnaws iron, bites steel;
Grinds hard stones to meal;
Slay king, ruins town,
and beats a mountain down."