Random Puzzles 

Workings

Hint
One is the study of fossils.

Answer
Palaeontology, the study of fossils and Limnology, the study of lakes and rivers. There are others you might have chosen.

Workings

Hint
Fill the 9-litre container first.

Answer
Here are the contents of the containers after each stage:

A = 9 litres, B = 4 litres
A     B
9     0     fill A
5     4     fill B from A (leaving 5 litres in A)
5     0     empty B
1     4     fill B from A (leaving 1 litre in A)
1     0     empty B
0     1     fill B from A
9     1     fill A
6     4     fill B from A (only 3 more litres fit in B)
6     0     empty B

This leaves 6 litres in container A.

Workings

Hint
This is a very common sequence.

Answer
5.

The numbers represent the number of letters of the words ONE, TWO, THREE, etc. Therefore, the answer is the number of letters in the word EIGHT.

Workings

Hint
Don't let this one melt your brain.

Answer
This puzzle is a classic paradox.

You can wrangle with the logic for hours and never reach an absolute conclusion.