Light the Lights

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

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.

Do you get any surprises?

What are the four rules?

What is the smallest number which lights them all up?