Random Puzzles 

Workings

Hint
How many 1x1 squares are there?

Answer
91 squares.

Reasoning
Squares of size:
   1 x 1 = 36
   2 x 2 = 25
   3 x 3 = 16
   4 x 4 = 9
   5 x 5 = 4
   6 x 6 = 1

Total = 36 + 25 + 16 + 9 + 4 + 1 = 91.

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
What could cause the egg to break, and how can we prevent this?

Answer
If we drop the egg from somewhere above 30 feet high, the egg can fall 30 feet and be caught, while still above the floor.

Workings

Hint
Think of the pages from 1-9, and then 10-99.

Answers
There are 147 pages. The number 3 appears 35 times.
Answer #1
For pages 1-9, there are 9 pages, which is 9 digits.

For pages 10-99, there are 90 pages, which is 180 digits.

This is a total so far of 189, therefore we require another 333 – 189 = 144 digits, which is another 144 ÷ 3 = 48 pages.

Taking us to 9 + 90 + 48 = 147 pages in total.

Answer #2
From page 1 to 147 we have 15 pages that end in 3:

   3, 13, 23, …, 143

We also have the ten pages that start with 30:

   30, 31, 32, …, 39

Plus the ten pages that start with 130:

   130, 131, 132, …, 139

For a total of 15 + 10 + 10 = 35 number 3's.