Random Puzzles 

Workings

Hint
Think laterally!

Answer
The outside!

Workings

Hint
Try writing the numbers out as letters.

Answer
45.

Reasoning
Each term increases by the number of letters in the previous term (ignoring any hyphens).
1  + length("ONE")       = 4
4  + length("FOUR")      = 8
8  + length("EIGHT")     = 13
13 + length("THIRTEEN")  = 21
21 + length("TWENTYONE") = 30
30 + length("THIRTY")    = 36
36 + length("THIRTYSIX") = 45

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 at the letter positions in the alphabet.

Answer
R.

If you take the alphabetic positions of each letter in a row, the total is always 56.

Double-Checking
Y + G + W + A = 25 +  7 + 23 +  1 = 56
K + L + R + O = 11 + 12 + 18 + 15 = 56
Z + J + P + D = 26 + 10 + 16 +  4 = 56
V + F + T + H = 22 +  6 + 20 +  8 = 56