Random Puzzles 

Workings

Hint
Look at Digit 3 first.

Answer
6394.

Reasoning
Labelling the clues:

Digit 2 is smaller than Digit 4 Digit 4 is two thirds of Digit 1 Digit 1 is two thirds of Digit 3 Digit 3 is three times Digit 2
Using (4), Digit 3 can only be 3, 6 or 9 (as it's 3 x Digit 2).

Therefore, using (4), Digit 2 can only be 1, 2 or 3.

Using (3), Digit 1 can only be 2, 4 or 6 (as it's two thirds of Digit 3).

However, using (2), the only possible value for Digit 1 that we can find two thirds of is 6.

So, using (2), Digit 4 is 4.

So far, we have 6??4.

Using (3), Digit 1 is two thirds of Digit 3, so Digit 3 must be 9.

And, by (4), Digit 2 must be 3.

Giving 6394.

Workings

Hint
How many students study chemistry and physics, but not biology?

Answer
500 students.

Reasoning
The answer is more easily seen if three intersecting circles are drawn, and the numbers inside each section are worked out.

We know that 73 students study all three disciplines, which allows us to work out the numbers.

97 students study chemistry and physics, so 97 - 73 = 24 study just chemistry and physics.
138 students study physics and biology, so 138 - 73 = 65 study just physics and biology.
152 students study chemistry and biology, so 152 - 73 = 79 study just chemistry and biology.

280 students study chemistry, so 280 - 73 - 24 - 79 = 104 study just chemistry.
254 students study physics, so 254 - 73 - 24 - 65 = 92 study just physics.
280 students study biology, 280 - 73 - 65 - 79 = 63 study just biology.

For a total of: 104 + 92 + 63 + 24 + 65 + 79 + 73 = 500 students.

Workings

Hint
How many 8x8 squares are there, what about 7x7.

Answer
1,296 rectangles and 204 squares.

Workings

Hint
Think of chickens.

Answer
Don't count your chickens until they're hatched.