Random Puzzles 

Workings

Hint
There are three feet in a yard, and 1,760 yards in a mile.

Answer
Seconds in a week.

Reasoning
There are 60 x 60 x 24 x 7 = 604,800 seconds in a week.

There are 3 x 1760 x 100 = 528,000 feet in 100 miles.

Workings

Hint
How many 1 x 1 squares are there, how many 2 x 2, …?

Answer
2,870 squares.

Reasoning
We have squares sizes from 1 x 1 up to 20 x 20, and these are the counts:
 1 x  1 = 400
 2 x  2 = 361
 3 x  3 = 324
 4 x  4 = 289
 5 x  5 = 256
 6 x  6 = 225
 7 x  7 = 196
 8 x  8 = 169
 9 x  9 = 144
10 x 10 = 121
11 x 11 = 100
12 x 12 =  81
13 x 13 =  64
14 x 14 =  49
15 x 15 =  36
16 x 16 =  25
17 x 17 =  16
18 x 18 =   9
19 x 19 =   4
20 x 20 =   1

Total = 400 + 361 + 324 + 289 + 256 + 225 + 196 + 169 + 144 + 121 + 100 + 81 + 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 2870.

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.

Workings

Hint
In each word, exactly one letter is wrong.

Answer
I like bees. When I see a bee, it makes me think of the honey that they make. Honey makes my toast nice.