Random Puzzles 

Workings

Hint
Fill the 9-litre container first.

Answer
Here are the contents of the containers after each stage:

A = 9 litres, B = 4 litres
A     B
9     0     fill A
5     4     fill B from A (leaving 5 litres in A)
5     0     empty B
1     4     fill B from A (leaving 1 litre in A)
1     0     empty B
0     1     fill B from A
9     1     fill A
6     4     fill B from A (only 3 more litres fit in B)
6     0     empty B

This leaves 6 litres in container A.

Workings

Hint
The piece ends with the word AWAY.

Answer
Little Miss Muffet
Sat on a tuffet,
Eating her curds and whey:
There came a big spider
Who sat down beside her
And frightened Miss Muffet away.

Workings

Hint
A little algebra might help.

Answer
¹/₈.

Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 – 3) x 4 – n = 20

Expanding the brackets and simplifying gives:

(2n^2 + 8 – 3) x 4 – n = 20

    (2n^2 + 5) x 4 – n = 20

         8n^2 + 20 – n = 20

              8n^2 – n = 0 (*)

                8n – 1 = 0

                    8n = 1

                     n = ¹/₈

In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.

Double-Checking
                 ¹/₈
   squared     = ¹/₆₄
   add 4       = 4¹/₆₄
   double      = 8¹/₃₂
   take away 3 = 5¹/₃₂
   times 4     = 20¹/₈

   subtracting ¹/₈ gives 20, as required.

Workings

Hint
Where do they each grow?

Answer
Potato.

This is the only one that grows underground.