Random Puzzles 

Workings

Answer
The words are open, pane, ends, nest.

Workings

Hint
A little algebra might help.

Answer
Pineapple = 83p, coconut = 57p, melon = 62p.

Reasoning
If we assign the letters P, C and M to the fruits, and work in pence we have:

(1)   M + C = 119
(2)   M + P = 145
(3)   C + P = 140

Using (2) − (1) we have:

(4)   P − C = 26

And (3) + (4) gives:

         2P = 166
          P = 83

This can then be substituted back into (2) and (3).

Workings

Hint
Look for the question.

Answer
N.

Reasoning
Starting with the first letter and taking every other letter gives: TO BE OR NOT TO BE TH

Starting with the second letter and taking every other letter gives: AT IS THE QUESTIO

Combining gives: TO BE OR NOT TO BE THAT IS THE QUESTIO, and the last letter of QUESTION is missing.

Workings

Hint
There are no squares of size 5 x 5.

Answer
There are 125 squares without a rook.

Reasoning
61 squares of size 1 x 1
39 squares of size 2 x 2
20 squares of size 3 x 3
 5 squares of size 4 x 4

Giving a total of 61 + 39 + 20 + 5 = 125 squares.