Random Puzzles 

Workings

Hint
Work out the total number of legs.

Answer
23 children (46 legs).

With 230 ants (1380 legs), 3 puppies (12 legs), and 1 teacher (2 legs).

If we call the number of puppies P, then there were (P + 20) children and 10 x (P + 20) ants, and a single teacher. If we now count the legs, we get:
Puppies:
 P x 4 =  4P

Children:
 (P + 20) x 2 =  2P + 40

Ants:
 10 x (P + 20) x 6 = 60P + 1200

Teacher: 2

A total of 66P + 1242

Giving:

 66P + 1242 = 1440

 66P        = 198

   P        = 3

So there were 3 puppies, hence 23 children.

Workings

Hint
Look closely at the beginnings and the ends of the words.

Answer
Ice.

Each word begins with the last two letters of the previous word.

Workings

Hint
Try this with a real board.

Answer
5 queens are required.

Workings

Hint
Be careful!

Answer
If you think that you are now in first place, then think again!

If you overtake the person in second place, you are now in second place yourself!