Charlie's Delightful Machine

Note: if you have an iPod Touch, iPhone, or iPad, or have Safari on your phone, there's a webapp called 'Light Delights' that you can use instead of the machine below.

Below 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.
To start again with a new set of rules, click the Restart button.





Try to make all four lights light up at once.

If you find an example where it's impossible to light them all up, send us the four rules and explain why it's not possible.

If you find an example where it is possible to light them all up, send us the four rules and the numbers that work.
What is special about your numbers?
What is the smallest number which lights them all up?