Random Puzzles 

Workings

Hint
How many rooms can Alex clear in 36 hours?

Answer
12 hours.

Reasoning
In 36 hours, Alex could empty 2 lots of bookshelves, Billie could also empty 2 lots of bookshelves, and Drew could refill 1 lot of bookshelves.

So, 2 + 2 − 1 = 3 lots of bookshelves in 36 hours. Which is 12 hours for one lot of bookshelves.

Alternative Reasoning
Alex and Billie can each empty ¹/₁₈ of the bookshelves in 1 hour, but Drew will refill ¹/₃₆ of the bookshelves in one hour.

So in one hour we have ¹/₁₈ + ¹/₁₈ − ¹/₃₆ = ¹/₁₂.

So it would take 12 hours to empty the bookshelves.

Workings

Hint
There are at least 4 answers that fit the question.

Answer
A hole or a vacuum, or perhaps a set of scales, or maybe a shadow.

Workings

Hint
Say each number, one digit at a time.

Answer
11131221141113122112.

Reasoning
Each term describes the previous term.

For example, 42 = one four, one two = 1412.

And, 1412 = one one, one four, one one, one two = 11141112.

Workings

Hint
I bought at least 5 of every stamp.

Answer
Five lots of 2p, 7p and 15p, and six lots of 10p, and 20p.

Reasoning
The shopkeeper rightly figured that I required five lots of all of the stamps, which came to (2p + 7p + 10p + 15p + 20p) x 5 = £2.70.

For two of the stamps I needed one more of each, and these must have added to the remaining 30p, so can only have been the 10p and 20p stamps.