Random Puzzles 

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
The sons row across first.

Answer
The two sons rowed to safety first, one son rowed back.
I rowed to safety and the other son rowed back to the island.
The two sons rowed to safety first, one son rowed back again.
My wife rowed to safety and the other son rowed back.
Finally, the two sons rowed to safety.

Workings

Hint
Try removing the spaces between the numbers.

Answer
48 and 11.

Reasoning
These are the squares of numbers without the correct spacing.

   1 4 9 16 25 36 49 64 81 100

with no spaces becomes:

   149162536496481100

broken into blocks of two:

   14 91 62 53 64 96 48 11 00

So the next two in the sequence are 48 and 11.

Workings

Hint
Fill the 9-litre container first.

Answer
Here are the contents of the containers after each stage:

A = 9 litres, B = 4 litres
A     B
9     0     fill A
5     4     fill B from A (leaving 5 litres in A)
5     0     empty B
1     4     fill B from A (leaving 1 litre in A)
1     0     empty B
0     1     fill B from A
9     1     fill A
6     4     fill B from A (only 3 more litres fit in B)
6     0     empty B

This leaves 6 litres in container A.