Random Puzzles 

Workings

Hint
A very common sequence is hidden here.

Answer
Badger.

Reasoning
The length of the words is the same length as the months of the year.
   gorilla  = 7 = January
   hedgehog = 8 = February
   camel    = 5 = March
   mouse    = 5 = April
   fox      = 3 = May
   bear     = 4 = June
   mole     = 4 = July
   badger   = 6 = August

Workings

Hint
The first in the list would be Hydrogen.

Answer
Fluorine.

These are the elements in atomic number order.

Workings

Hint
Pages 1 to 9 are one digit each.

Answer
There are 65 pages, and the number 9 appears six times.

Reasoning
The first 9 pages each require one digit per page, which leaves 112 digits remaining. This requires an additional 112 ÷ 2 = 56 more pages. For a total of 9 + 56 = 65 pages.

Each block of ten contains a single 9, for a total of six 9's (as we've only reached page 65, and we don't have to worry about pages 90 to 99 either).

Double-Checking
The 65 pages are (with the six 9's highlighted):

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65.

If we remove the spaces, we get:

1​2​3​4​5​6​7​8​9​1​0​1​1​1​2​1​3​1​4​1​5​1​6​1​7​1​8​1​9​2​0​2​1​2​2​2​3​2​4​2​5​2​6​2​7​2​8​2​9​3​0​3​1​3​2​3​3​3​4​3​5​3​6​3​7​3​8​3​9​4​0​4​1​4​2​4​3​4​4​4​5​4​6​4​7​4​8​4​9​5​0​5​1​5​2​5​3​5​4​5​5​5​6​5​7​5​8​5​9​6​0​6​1​6​2​6​3​6​4​6​5​. Which is 121 digits.

Workings

Hint
At each stage, a new dot appears at the top.

Answer
 


Reasoning
At each stage, a new dot starts at the top. The first dot moves clockwise, the second dot moves counter-clockwise, the third dot moves clockwise, etc.