Random Puzzles 

Workings

Hint
How large would the smaller cube be?

Answer
1,352 small cubes.

Reasoning
The original large cube with 16 small cubes along each edge would require 16 x 16 x 16 = 4,096 small cubes.

Removing the outside layer would leave a large cube now with 14 small cubes along each edge (which requires 14 x 14 x 14 = 2,744 small cubes).

It isn't 15 small cubes because you're removing both ends of an edge.

Therefore, you have removed 4,096 − 2,744 = 1,352 small cubes.

Workings

Hint
The first letters of the names are: G, R, E, P, M, E, A, A.

Answer
gl    = Gail
rs    = Rose or Iris
dth   = Edith
ptsy  = Patsy
mxn   = Maxine
dwn   = Edwina or Dawn
gth   = Agatha
dry   = Audrey

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
Look to the skies.

Answer
NE.

From Neptune. The first two letters from the planets in sequence: MErcury, VEnus, EArth, MArs, JUpiter, SAturn, URanus, NEptune.