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
This question involves the months of the year in some way.

Answer
4 3 1.

Reasoning
This is the sequence of the length of the name of the month, and the number of days in that month.

7 3 1 = January, which has 7 letters, and 31 days.

8 2 8 = February, which has 8 letters, and 28 days.

5 3 1 = March, which has 5 letters, and 31 days.

5 3 0 = April, which has 5 letters, and 30 days.

3 3 1 = May, which has 3 letters, and 31 days.

4 3 0 = June, which has 4 letters, and 30 days.

Which means the next three digits are:

4 3 1 = July, which has 4 letters, and 31 days.

Workings

Hint
You can only go up, or right.

Answer
6.

With U = Up, and R = Right, you can move in the following ways:
UURR
URUR
URRU
RUUR
RURU
RRUU

Workings

Hint
There are three feet in a yard, and 1,760 yards in a mile.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 3 x 1760 x 100 = 528,000 feet in 100 miles.