Random Puzzles 

Workings

Hint
This is a well known nursery rhyme.

Answer
HDD.

The initial letters from the nursery rhyme, Hickory Dickory Dock.
Hickory, dickory, dock,
The mouse ran up the clock,
The clock struck one,
The mouse ran down,
Hickory, dickory, dock.

Workings

Hint
The answer is right in front of you.

Answer
Mississippi.

The diagram is actually the word 'mississippi' on its side.

Workings

Hint
Try finding the cube root of 190,747.

Answer
53, 59, and 61.

Reasoning
Start by taking the cube root of 190,747, which is approximately 57.56.

The next highest prime number is 59:

   190,747 ÷ 59 = 3,233

Let's try the next prime number, which is 61:

     3,233 ÷ 61 = 53

53, 59, and 61, are all prime, and are consecutive, so this is the answer.

Double-Checking
   53 x 59 x 61 = 190,747

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.