
In Sam and Jill's garden there are two sorts of ladybirds. There are red Seven-Spot ladybirds with $7$ black spots and shiny black Four-Spot ladybirds with $4$ red spots.

Sam and Jill looked at a leaf with three ladybirds on it.

"One Seven-Spot ladybird," said Sam, "and two
Four-Spot ones."
"That's $15$ spots altogether!" laughed Jill. "I wonder if we could
find ladybirds whose spots add to other numbers. I know how to do
$16$."
"And $14$ is easy too," added Sam.
How would you make $16$ and $14$ spots with the Seven-Spot and Four-Spot ladybirds?
What other numbers under $30$ can you make with
$4$s and $7$s?
Which ones are impossible?
Published September 2003.