Random Puzzles 

Workings

Hint
How many rats can one cat catch in 5 minutes?

Answer
5.

  5 cats can catch 5 rats in 5 minutes.

So

  1 cat can catch 1 rat in 5 minutes.

  1 cat can catch 2 rats in 10 minutes.

  1 cat can catch 20 rats in 100 minutes.

Therefore

  5 cats can catch 100 rats in 100 minutes.

Workings

Hint
Look at the first letters of the words.

Answer
Alphabet.

The first letters of the words are spelling BrainBashers.

Workings

Hint
Try a random number of over 50s to see what happens.

Answer
20,064 apples.

Reasoning
It doesn't matter how old the people are.

As only ³/₄ of the over 50s claimed 16 apples, this averages out to 12 apples each.

Similarly, only ¹/₈ of the under 50s claimed 96 apples, this again averages out to be 12 apples each.

Therefore, the total number of apples was 1,672 x 12 = 20,064.

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.