Random Puzzles 

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
The first letters of the words are: C, S, P, B. One of the vegetables is another word for rutabaga.

Answer
Carrot, swede, pea, bean.

Swede is another word for rutabaga.

Workings

Hint
Try to rotate them around in your head, but watch out for mirror images.

Answer
A and C.

Workings

Hint
The answer is not 15.

Answer
19 bottles.

Reasoning
From the initial 77 bottles, 75 bottles can be recycled for 15 new full bottles.

Once those are drunk, Alex will have 17 empty bottles (15 plus the 2 extra empty bottles).

From the 17 empty bottles, 15 bottles can be recycled for 3 new full bottles.

Once those are drunk, Alex will have 5 empty bottles (3 plus the 2 extra empty bottles), which can be recycled for one final full bottle.

Giving a total of 15 + 3 + 1 = 19.