What is more useful when it is broken?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

What is the next number in this matchsticks series riddle?

John is on an island and there are three crates of fruit that have washed up in front of him. One crate contains only apples. One crate contains only oranges. The other crate contains both apples and oranges.

Each crate is labelled. One reads 'apples', one reads 'oranges', and one reads 'apples and oranges'. He know that NONE of the crates have been labeled correctly - they are all wrong.

If he can only take out and look at just one of the pieces of fruit from just one of the crates, how can he label all of the crates correctly?

1 + 9 + 8 = ?
considering, 28 + 8 + 92 = 10

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?

Count the number of triangles in the below picture?

One absent-minded ancient philosopher forgot to wind up his only clock in the house. He had no radio, TV, telephone, internet, or any other means for telling time. So he travelled on foot to his friend's place a few miles down the straight desert road. He stayed at his friend's house for the night and when he came back home, he knew how to set his clock. How did he know?

Why is a river so rich ?