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
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
One of the words is clockwise.

Answers
foo + tpr + int = footprint
som + ewh + ere = somewhere
pin + eap + ple = pineapple
tec + hni + que = technique
ref + ere + nce = reference
pro + fes + sor = professor
bio + gra + phy = biography
clo + ckw + ise = clockwise
bar + ome + ter = barometer

Workings

Hint
Remember that a quarter is 25c, a dime is 10c and a nickel is 5c.

Answer
92 of each coin.

Reasoning
There are an equal number of quarters, dimes and nickels, so we know that the answer must be a multiple of:

   25c + 10c + 5c = 40c

and:

   3680c ÷ 40c = 92 coins.