Between them Catrin, Amie and Kate have 18 bottles of nail varnish. Amie has twice as many as Catrin, and Kate has three times as many as Catrin.
How many does Catrin have?
Let's call the number of nail varnish bottles Catrin has as C.
Amie has twice as many as Catrin, so Amie has 2C.
Kate has three times as many as Catrin, so Kate has 3C.
Together, they have C + 2C + 3C = 6C bottles of nail varnish.
We know that the total number of bottles is 18, so we can write the equation 6C = 18.
Dividing both sides of the equation by 6, we get C = 18/6 = <<18/6=3>>3.
Therefore, Catrin has 3 bottles of nail varnish. Answer: \boxed{3}.
Let's assume the number of nail varnishes Catrin has as x.
According to the given information, Amie has twice as many as Catrin. Therefore, Amie has 2x nail varnishes.
Kate has three times as many as Catrin. Therefore, Kate has 3x nail varnishes.
The total number of nail varnishes they have together is 18.
So the equation becomes:
x + 2x + 3x = 18
Combining like terms, we get:
6x = 18
Dividing both sides by 6, we get:
x = 3
Therefore, Catrin has 3 bottles of nail varnish.