Random Puzzles 

Workings

Hint
The answer involves multiplication (for example, 9 x 8 = 72).

Answer
468.

Reasoning
If we split each line in the following way:

98 68 88
72 48 64
14 32 24

Each new line is generated by multiplying the digits two at a time and writing the result below.

For example, 9 x 8 = 72, so 72 appears directly below 98.

And 7 x 2 = 14, so 14 appears directly below 72.

Double-Checking
9 x 8 = 72, 7 x 2 = 14, 1 x 4 = 4.

6 x 8 = 48, 4 x 8 = 32, 3 x 2 = 6.

8 x 8 = 64, 6 x 4 = 24, 2 x 4 = 8.

Workings

Hint
Look at the start of each word.

Answer
augment.

The first three letters are the same as the first three letters of the months in order.

Workings

Hint
Find how many sheep Drew has first.

Answer
3.

Reasoning
If we denote Alex by A, Billie by B, Charlie by C, and Drew by D and number the clues.

If Alex had three more sheep, then he'd have one fewer sheep than Billie. Whereas Drew has the same number as the other three shepherds put together. If Charlie had three fewer sheep, he'd have exactly three times the number of Alex. If they were evenly distributed, they'd each have eleven sheep.
By (4):
   A + B + C + D = 44

And, by (2), these are shared equally between A + B + C and D.

So D = 22, and A + B + C = 22 (*)

By (1):
   A + 3 = B − 1
   A + 4 = B

By (3):
   C − 3 = 3A
   C     = 3A + 3

Substitute B and C in (*):

A + (A + 4) + (3A + 3) = 22
                5A + 7 = 22
                    5A = 15
                     A = 3

And, B = 7, C = 12.

Double-Checking
A = 3, B = 7, C = 12, D = 22.

(1) 3 + 3 = 7 − 1
(2) 3 + 7 + 12 = 22
(3) 12 − 3 = 3 x 3
(4) 3 + 7 + 12 + 22 = 44, and 44 ÷ 4 = 11 each.

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.