Random Puzzles 

Workings

Hint
Try removing the spaces between the numbers.

Answer
48 and 11.

Reasoning
These are the squares of numbers without the correct spacing.

   1 4 9 16 25 36 49 64 81 100

with no spaces becomes:

   149162536496481100

broken into blocks of two:

   14 91 62 53 64 96 48 11 00

So the next two in the sequence are 48 and 11.

Workings

Hint
From the 1 go straight down.

Answer
 

Workings

Hint
Do leap years make a difference?

Answer
Hours in 10 years.

Reasoning
In a day, there are 60 x 60 x 24 seconds = 86,400 seconds.

In 10 years, there are 10 x 365 x 24 hours = 87,600 hours, which even without the leap years is already the larger number.

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.