Random Puzzles 

Workings

Hint
A little 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
How many bricks are laid in six hours?

Answer
1 hour.

Reasoning
How many bricks are laid in six hours?

In six hours, Kevin lays 1000 bricks, Freddie lays 2000 bricks, and Jimmy lays 3000 bricks.

So, in six hours, we have a total of 6000 bricks laid.

Which means, on average, that it will take one hour to lay 1000 bricks.

Workings

Hint
The first nine prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23.

Answer
29.

The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Workings

Hint
The answer is a whole number less than 10.

Answer
3.

Reasoning
We can multiply throughout by 12,
    X     X     X     X
    -  -  -  +  -  =  -
    X     2     4     12

to give:

   12 − 6X + 3X = X

        12 − 3X = X

             12 = 4X

              3 = X

As required.

Double-Checking
    3     3     3     3
    -  -  -  +  -  =  -
    3     2     4     12

    1 − 1.5 + 0.75 = 0.25

              0.25 = 0.25, which confirms that 3 is correct.