Challenge Level

This problem is similar to Light the Lights, but slightly more tricky. You may like to try that one first.

Here is a machine with four coloured lights. Each light responds to a rule.

When you type in a number, lights go on if their rule is satisfied.

If the number satisfies more than one rule, then more than one colour will light up.

Type in some numbers and see which lights you can switch on.

What is the smallest number which lights up all the lights?