Random Puzzles 

Workings

Hint
If Alex had committed the crime, how many lies would there be?

Answer
Chris committed the crime.

Reasoning
We know that exactly 4 lies were told.

If it was Alex, then 3 lies would have been told (by those who said it wasn't Alex).

If it was Billie, then 2 lies would have been told.

If it was Chris, then 4 lies would have been told.

If it was Drew, then 3 lies would have been told.

If it was Emery, then 3 lies would have been told.

If it was Frankie, then 3 lies would have been told.

Therefore, it can only have been Chris.

Double-Checking
Since it was Chris, there were 14 truths, and 4 lies, for a total of 18 clues.

Workings

Hint
There are 3 P's, so there are 3 different ways to start the word.

Answer
960.

Reasoning
Given: P P P U U Z Z Z Z Z L L L L E S S.

The order of the Z's is important. For example, we could chose a red one and a green one, so the order they appear in the sign has to be taken into consideration.

There are:
   3 different P's that could be chosen.
   2 different U's that could be chosen.
   5 different Z's that could be chosen.
   4 different Z's that could be chosen, as one has already been chosen.
   4 different L's that could be chosen.
   1 E that could be chosen.
   2 different S's that could be chosen.

So there are 3 x 2 x 5 x 4 x 4 x 1 x 2 = 960 different ways to make the sign.

Workings

Hint
There are at least 4 answers that fit the question.

Answer
A hole or a vacuum, or perhaps a set of scales, or maybe a shadow.

Workings

Hint
This is a well known nursery rhyme.

Answer
AJCTA.

These are the initial letters from the nursery rhyme 'Jack and Jill went up the hill'. The letters represent 'and Jill came tumbling after'.