Random Puzzles 

Workings

Hint
Does the number of adults and children matter?

Answer
3,672.

Reasoning
The actual number of adults and children doesn't actually matter.

If all of the people were adults, then half of them (306) would be given 12 sweets:

  306 x 12 = 3672

If all of the people were children, then three quarters of them (459) would be given 8 sweets:

  459 x  8 = 3672

If there were 512 adults (so 256 would get 12 sweets = 3072) and 100 children (so 75 would get 8 sweets = 600):

  256 x 12 + 75 x 8 = 3672

We can change the numbers of adults and children, but it doesn't change the answer.

The reason for this lies in the fact that ¹/₂ adults x 12 sweets = ³/₄ children x 8 sweets (both are 6).

Workings

Hint
The piece ends with the word AWAY.

Answer
Little Miss Muffet
Sat on a tuffet,
Eating her curds and whey:
There came a big spider
Who sat down beside her
And frightened Miss Muffet away.

Workings

Hint
Look at the first few characters of each word.

Answer
augment.

The first three letters are the same as the first three letters of the months in order.

Workings

Hint
Count carefully.

Answer
5.

Three daughters and two sons.