Mathematical Puzzles 

Workings

Hint
A little bit of algebra might help.

Answer
64 pounds.

The head weighs 24 pounds, the body weighs 32 pounds, and the tail weighs 8 pounds.

Reasoning
The trout is made up of the head, body and tail, H, B and T.

We are told that:

    T = 8

(1) H = T + B ÷ 2

(2) B = H + T

Placing T into (1) and (2) we get:

(3) H = 8 + B ÷ 2

(4) B = H + 8

Using (4) in (3) we get:

    H = 8 + B ÷ 2

(5) H = 8 + (H + 8) ÷ 2

Multiplying (5) by 2 we get:

 2H = 16 + H + 8

 2H = 24 + H

  H = 24

Therefore, by (2):

 B = H + T

 B = 24 + 8

 B = 32

Giving:

 H = 24
 B = 32
 T = 8

And a total of 24 + 32 + 8 = 64 pounds.

Workings

Hint
The lowest route contains more 2's than the highest route.

Answers
Highest = 24. Lowest = 12.

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
You can't move diagonally.

Answer
5.

Reasoning
Starting with the central F, you can move:

Up (D), Up (I), Left (N).
Left (N), Left (I), Left (D).
Left (N), Left (I), Up (D).
Down (D), Left (N), Left (I).
Down (D), Down (I), Down (N).