Random Puzzles 

Workings

Hint
The four items form a complete list.

Answer
Spring, summer, autumn and winter.

Workings

Hint
Where was Dave standing when he fell?

Answer
Dave fell off the very bottom rung of the ladder!

Workings

Hint
You don't need to use a calculator.

Answer
Cube root of 2.

Reasoning
We could use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.

But, if you've not got your calculator handy…

We have:

   10^1/₁₀ or 2^1/₃

Raise each to the power of 30 (since 10 x 3 = 30) to give:

   (10^1/₁₀)³⁰ or (2^1/₃)³⁰

   10^{1/₁₀ x 30} or 2^{1/₃ x 30}

   10³ or 2¹⁰

   1000 or 1024

Therefore, the cube root of 2 is larger.

Workings

Hint
The first letter can only be B.

Answer
A badger.

Reasoning
My first is in bridge, but not in ridge = B

My second is in awake, and in mistake = A K E

My third is in danger, but not in ranger = D

My fourth is in strange, and in orange = R A N G E

My fifth is in spline, and in nine = I N E

My last is in river, and in diver = R I V E