Random Puzzles 

Workings

Hint
There are over 20 mistakes.

Answer
21.

Reasoning
Many years ago, before modern education in the new millennium, one problem in schools was basic spelling and grammar. To combat this and raise achievement, teachers were advised to start at the very beginning, at the youngest age. Once they had managed to breathe new life into lessons, progress came quickly, success was then guaranteed. How many spelling errors would modern scholars identify in this passage?

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 vs 2^1/3

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

   (10^1/10)³⁰ vs (2^1/3)³⁰

   10^{1/10 x 30} vs 2^{1/3 x 30}

   10³ vs 2¹⁰

   1000 vs 1024

Therefore, the cube root of 2 is larger.

Workings

Hint
There are no squares of size 5x5.

Answer
There are 125 squares without a rook.

Reasoning
There are 61 squares of size 1x1.
There are 39 squares of size 2x2.
There are 20 squares of size 3x3.
There are  5 squares of size 4x4.

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

Workings

Hint
Try removing some letters.

Answer
Carrot.

Reasoning
Each of the other words remains a real word if you remove the first and last letter:
s-event-y b-raw-l c-love-r p-rope-r c-arro-t * s-win-g e-merge-d c-raft-y t-rave-l s-acre-d s-ton-e p-lung-e