Easy Puzzles 

Workings

Hint
Try working backwards.

Answer
335 strawberries.

Reasoning
Working backwards...

I ended up with 34 strawberries, so I had 102 before giving Charlie two thirds.

I ate 6 myself, so I had 108 before I ate those.

I had 108 strawberries, so I had 162 before giving Billie one third.

I ate 3 myself, so I had 165 before I ate those.

I had 165 strawberries, so I had 330 before giving Alex one half.

Ate 5 myself, so I had 335 before I ate those.

Therefore, I started with 335 strawberries.

Double-Checking
I started with 335.

I ate 5, leaving 330.

I gave Alex half (165), leaving 165.

I ate 3, leaving 162.

I gave Billie one third (54), leaving 108.

I ate 6, leaving 102.

I gave Charlie two thirds (68), leaving 34.

Workings

Hint
Look backwards.

Answer
nogatco.

Reasoning
These are geometric shapes, the number of sides increases, and the words are reversed.
3 elgnairt = triangle
4 erauqs   = square
5 nogatnep = pentagon
6 nogaxeh  = hexagon
7 nogatpeh = heptagon
8 nogatco  = octagon

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
There are no larger squares than size 4x4.

Answer
There are 110 squares without a rook.

Reasoning
There are 60 squares of size 1x1.
There are 35 squares of size 2x2.
There are 12 squares of size 3x3.
There are  3 squares of size 4x4.

Giving a total of 60 + 35 + 12 + 3 = 110 squares.