Random Puzzles 

Workings

Hint
What can digits 4 and 5 be?

Answer
71842.

Reasoning
The number can be represented as:

   - - - - -

By (5), Digit 5 is half of Digit 4, so we have four possibilities:

   - - - 2 1
   - - - 4 2
   - - - 6 3
   - - - 8 4

By (4), Digit 1 is higher than the sum of Digit 4 and Digit 5, so we can eliminate two possibilities, leaving:

   - - - 2 1
   - - - 4 2

By (7), Digit 5 is between Digit 2 and Digit 1, so we can eliminate - - - 2 1, leaving:

   - - - 4 2

By (4), Digit 1 must be higher than the sum of Digit 4 and Digit 5, so we have three possibilities:

   7 - - 4 2
   8 - - 4 2
   9 - - 4 2

By (6), Digit 1 is 1 smaller than Digit 3 we can eliminate 9 - - 4 2, and fill in Digit 3, leaving:

   7 - 8 4 2
   8 - 9 4 2

By (3), Digit 2 is the lowest digit, and must be 1:

   7 1 8 4 2
   8 1 9 4 2

By (1), the only possibility is:

   7 1 8 4 2

Workings

Hint
Adding just one should be enough.

Answer
Holes!

Workings

Hint
Convert the letters to positions in the alphabet.

Answer
M.

Reasoning
These are letters that occupy prime number positions in the alphabet:
b =  2
c =  3
e =  5
g =  7
k = 11
m = 13 *
q = 17
s = 19
w = 23

Workings

Hint
Try working backwards.

Answer
148.

148 x 6 = 888.

The easiest way is to divide successive 8's by 6 until you get an integer:
  8 ÷ 6 = 1.3333
 88 ÷ 6 = 14.666
888 ÷ 6 = 148