Random Puzzles 

Workings

Hint
A little algebra might help.

Answer
Width=40, height=20, depth=18.

Reasoning
If we call the height H, the width W and the depth D we have:
   H x W = 800

       H = 800 ÷ W (1)

   W x D = 720

       W = 720 ÷ D (2)

   H x D = 360

       H = 360 ÷ D (3)

Using (1) and (3) we have:
   800   360
   ——— = ———
    W     D

   800 x D = 360 x W

Using (2):
   800 x D = 360 x 720
                   ———
                    D

   800 x D² = 259,200

         D² = 324

          D = 18

Using (2), W = 40.

Using (1), H = 20.

Workings

Hint
What can digits 4 and 5 be?

Answer
71842.

Reasoning
The number can be represented as:

   - - - - -

By (5), Digit 5 is half of Digit 4, so we have four possibilities:

   - - - 2 1
   - - - 4 2
   - - - 6 3
   - - - 8 4

By (4), Digit 1 is higher than the sum of Digit 4 and Digit 5, so we can eliminate two possibilities, leaving:

   - - - 2 1
   - - - 4 2

By (7), Digit 5 is between Digit 2 and Digit 1, so we can eliminate - - - 2 1, leaving:

   - - - 4 2

By (4), Digit 1 must be higher than the sum of Digit 4 and Digit 5, so we have three possibilities:

   7 - - 4 2
   8 - - 4 2
   9 - - 4 2

By (6), Digit 1 is 1 smaller than Digit 3 we can eliminate 9 - - 4 2, and fill in Digit 3, leaving:

   7 - 8 4 2
   8 - 9 4 2

By (3), Digit 2 is the lowest digit, and must be 1:

   7 1 8 4 2
   8 1 9 4 2

By (1), the only possibility is:

   7 1 8 4 2

Workings

Hint
I have fewer than 10 children.

Answer
4.

I have three daughters and one son.

Workings

Hint
Be careful of what you're adding.

Answer
We have to be careful what we are adding together.

Originally, they paid £30, they each received back £1, they now have only paid £27.

Of this £27, £25 went to the manager for the room and £2 went to the porter.