Easy Puzzles 

Workings

Hint
Don't let this one melt your brain.

Answer
This puzzle is a classic paradox.

You can wrangle with the logic for hours and never reach an absolute conclusion.

Workings

Hint
The country spans more than one word.

Answer
England.

Alex's aches and pains felt worse because of swollEN GLANDs that had flared up during the night, perhaps a tonic would help?

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
Try working backwards.

Answer
15.

Reasoning
One quarter of 360 is 90.

One third of 90 is 30.

One half of 30 is 15.