Puzzle ZEXD 

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 - not allowed by (2)

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

   17 children, with 11 sweets each (*)

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

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