Random Puzzles 

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
Is a million grains of sand a heap?

Answer
We can probably agree on two things:

A million grains of sand is a heap.
If we remove one grain of sand from this heap, we will still have a heap.
We can now keep repeating (2) until we only have a single grain of sand remaining.

Is this a heap? Clearly not. But what went wrong with our thinking?

This is called the Sorites paradox (soros being Greek for "heap") and is a classic paradox that has no real answer.

Both (1) and (2) are true, and we can indeed keep removing one grain of sand until we have a single grain remaining. If we remove one more grain, we're left with nothing, is this still a heap?

When does the heap become a non-heap?

Workings

Hint
The first word starts with M.

Answer
Many a true word is said in jest.

Workings

Hint
Think about the items required to play each sport.

Answer
Badminton.

This is the only sport which does not use a ball, it uses a shuttlecock.