Random Puzzles 

Workings

Hint
Is there a missing letter?

Answer
The entire conundrum does not have the letter E.

However, it does contain every other letter.

Workings

Hint
Tops of thermometers can't be filled unless the bottoms are.

Answer
 

Workings

Hint
How many large pipes are required to drain the reservoir in 24 hours?

Answer
21 hours and 36 minutes.

Reasoning
Looking at the first clue:
   in 12 hours, 6 large pipes can drain 1 reservoir
   in 24 hours, 6 large pipes can drain 2 reservoirs
   (*) in 24 hours, 3 large pipes can drain 1 reservoir

Looking at the second clue:
   in 8 hours, 3 large + 9 small pipes can drain 1 reservoir
   in 24 hours, 3 large + 9 small pipes can drain 3 reservoirs

But, by (*), we know that in those 24 hours, 3 large pipes can drain 1 of those reservoirs.

Therefore, the other 2 reservoirs can be drained by the small pipes on their own:
   in 24 hours, 9 small pipes can drain 2 reservoirs
   in 24 hours, 1 small pipe can drain ²/₉ reservoirs
multiply the hours by 9:
   in 216 hours, 1 small pipe can drain 2 reservoirs
   in 216 hours, 5 small pipes can drain 10 reservoirs
divide the hours by 10:
   in 21.6 hours, 5 small pipes can drain 1 reservoir

21.6 hours = 21 hours and 36 minutes.

Workings

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

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

For pages 10 to 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.