Random Puzzles 

Workings

Answer
The words are open, pane, ends, nest.

Workings

Hint
A little bit of algebra might help.

Answer
There are four boys and three girls.

If we call the number of boys B, and girls G.

From the first statement (we take one off as Billy is a boy):

              B − 1 = G

and similarly:

        2 x (G − 1) = B

Substitute G from the first equation into the second equation to give:

  2 x ((B − 1) − 1) = B

    2 x (B − 1) − 2 = B

      2 x B − 2 − 2 = B

          2 x B − 4 = B

                  B = 4

which means that B = 4 and hence G = 3.

Workings

Hint
There are two sequences.

Answer
26.

There are two alternate series, starting with the first two numbers, and each formed by doubling the preceding number in its own series and subtracting 2.

Workings

Hint
This is a trick question.

Answer
Once.

After which you will be taking 7 from 42!