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
How many hands did the first person shake?

Answer
190.

The first person shook hands with 19 others, the second had already shook hands with the first and therefore shook 18 hands, etc: 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1 = 190.

Workings

Hint
The answer isn't very large at all.

Answer
There are four boys and six girls in the family.

If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b - 1) = g.

And his sister, Frankie, has one more sister than she has brothers, so g - 1 = b + 1.
    2(b - 1) = g       [1]
       g - 1 = b + 1   [2]

Using [1] in [2] gives:

2(b - 1) - 1 = b + 1

Expanding the bracket gives:

  2b - 2 - 1 = b + 1

Simplifying the left hand side gives:

     2b - 3  = b + 1

Add 3 to each side gives:

          2b = b + 4

Subtract b from both sides gives:

           b = 4

Using b = 4 in [1] gives:

    2(4 - 1) = g

           6 = g

Workings

Hint
The word MAY appears 39 times.

Answer
The word MAY appears 39 times.