Random Puzzles 

Workings

Hint
How much soil is in any hole?

Answer
None!

Workings

Hint
The word SEPTEMBER appears 17 times.

Answer
The word SEPTEMBER appears 17 times.

Workings

Hint
A little bit of algebra might help.

Answer
I asked for 7 feet, 4 inches, but Alex brought me 4 feet, 7 inches.

Reasoning
If we label what I asked for as A feet and B inches, which is (12 x A + B) inches, then I actually received B feet and A inches, which is (12 x B + A) inches. Which means that:

   ⁵/₈ x (12 x A + B) = (12 x B + A)

Simplifying gives:

   A = ⁹¹/₅₂ x B

As B is the number of inches, it can only be between 1 and 12 and must give A as a whole number of feet.

B = 4 is the only possible value, which means that A = 7.

So I originally asked for 7 feet, 4 inches.

Double-Checking
I received 4 feet, 7 inches = 55 inches.

I asked for 7 feet, 4 inches = 88 inches, and 88 x ⁵/₈ = 55.

Workings

Hint
At each stage, a new dot appears at the top.

Answer
 


Reasoning
At each stage, a new dot starts at the top. The first dot moves clockwise, the second dot moves counter-clockwise, the third dot moves clockwise, etc.