Random Puzzles 

Workings

Hint
Start by counting the letters you're already given.

Answers
This sentence contains one X. Slightly trickier, this sentence contains four R's. Even trickier, this sentence contains precisely ten E's. This sentence has exactly thirty-nine letters. This sentence, hopefully, contains seventy-five letters, one hyphen, five commas, and four Y's. To finish, if this sentence had a T removed, it would contain sixty-two letters!

Workings

Hint
The answer isn't very large at all.

Answer
There are four boys and six girls in the family.

If there were B boys, and G girls we know that Billy has twice as many sisters as brothers, so 2 x (b − 1) = g.

And his sister, Frankie, has one more sister than she has brothers, so g − 1 = b + 1.
    2(b − 1) = g       [1]
       g − 1 = b + 1   [2]

Using [1] in [2] gives:

2(b − 1) − 1 = b + 1

Expanding the bracket gives:

  2b − 2 − 1 = b + 1

Simplifying the left hand side gives:

     2b − 3  = b + 1

Add 3 to each side gives:

          2b = b + 4

Subtract b from both sides gives:

           b = 4

Using b = 4 in [1] gives:

    2(4 − 1) = g

           6 = g

Workings

Hint
Look at the start of each word.

Answer
augment.

The first three letters are the same as the first three letters of the months in order.

Workings

Hint
The first 5 words begin with D, A, E, W, T.

Answers
--lta = delta --yss = abyss --pty = empty --dth = width --day = today --ybe = maybe --dex = index or codex --fth = fifth --nda = panda --aph = graph --alp = scalp --era = opera --njo = banjo --eue = queue --xty = sixty