Random Puzzles 

Workings

Hint
A 3-letter word becomes a 4-letter word.

Answer
Red.

Reasoning
red + a = read.

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
Saturday.

Reasoning
It's best to work backwards:

   "Sunday's tomorrow"

is Monday.

   "the day after Sunday's tomorrow"

is therefore Tuesday.

   "five days before the day after Sunday's tomorrow"

is therefore Thursday.

   "yesterday was five days before the day after Sunday's tomorrow"

yesterday was Thursday, making today Friday. Therefore tomorrow is Saturday.

Workings

Hint
Look at the gaps in the alphabetic position.

Answer
V.

Skip three and two letters alternately.