Random Puzzles 

Workings

Hint
Find two numbers that multiply to 187.

Answer
There were 17 children, with 11 sweets each.

Reasoning
If we number the clues:
each child had more than one sweet there were more children than there were sweets per child
187 only has the factors 1, 11, 17, 187. Therefore, the only possible answers are:

   1 child, with 187 sweets each, which is not allowed by (2)

   11 children, with 17 sweets each, which is not allowed by (2)

   17 children, with 11 sweets each (*)

   187 children, with 1 sweet each, which is not allowed by (1)

Only one possible answer (*) isn't eliminated.

Workings

Hint
Try starting with the cube root of the number.

Answer
195 x 197 x 199.

Reasoning
Since we're after three numbers that multiply together, a good place to start is the cube root of 7,644,585, which is roughly 196.99.

Let's try dividing by the closest odd number to 196.99:

   7644585 ÷ 197 = 38805

We're now after whole divisors of 38,805, so trying either odd number either side of 197 might work.

Trying either 195 or 199 gives the answer.

Double-Checking
   195 x 197 x 199 = 7,644,585

Note
Trying the closest odd number to the cube root always works, and the other two numbers are the odd numbers either side.

Workings

Hints
Try: soot + tire, most + mare, much + pink.

Answers
soot + tire = tortoise
most + mare = marmoset
much + pink = chipmunk
area + tent = anteater
leap + then = elephant

Workings

Hint
Which letters look the same upside down and backwards?

Answer
NOON.