Random Puzzles 

Workings

Hint
Think outside the box.

Answer
Start from the top left dot, and go past the top right dot, and then diagonally down to the bottom left dot, back up to the top left dot, and diagonally down to the bottom right dot.

Workings

Hint
Try writing the numbers out as letters.

Answer
45.

Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1  + length("ONE")       = 4
4  + length("FOUR")      = 8
8  + length("EIGHT")     = 13
13 + length("THIRTEEN")  = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY")    = 36
36 + length("THIRTYSIX") = 45

Workings

Hint
How much of a warren can each rabbit dig in one hour?

Answer
2 hours.

Reasoning
The small rabbit can dig a warren in nine hours, so digs ¹⁄₉ in one hour.

The medium rabbit can dig a warren in 6 hours, so digs ¹⁄₆ in one hour.

The large rabbit can dig a warren in four and a half hours, so digs ¹⁄_4.5 in one hour.

   1 Hour = ¹⁄₉ + ¹⁄₆ + ¹⁄_4.5

To make the denominators all the same, we can multiply through by ¹⁸⁄₁₈ to give:

   1 Hour = ²⁄₁₈ + ³⁄₁₈ + ⁴⁄₁₈

   1 Hour = ⁹⁄₁₈

   1 Hour = ¹⁄₂

So in one hour, they have dug half a warren, the whole warren will therefore take 2 hours.

Workings

Hint
'in the back of the net' begins with the letter G.

Answers
good = not bad
wood = forest
wool = sock material
cool = not hot
cowl = hooded robe
coil = spiral of wire
soil = earthy ground
foil = roasting metal
foal = baby horse
goal = in the back of the net