I noticed that blue only lights up for the first 5, and in the grid of when each lights turn on, none of the numbers turn on at the same time in the first 5 numbers. This means that it is impossible to turn them all on at the same time with a positive number.
This made me wonder if it was impossible. But I knew that Nrich wouldn’t have an impossible question. So there must be answer. After thinking for a while, I realised that blue would probably turn on in the negatives. No negative number could be bigger than a positive number. However it is impossible to tell what the smallest number is, as all 4 lights could potentially turn on at negative infinity or more, meaning that I cannot say what the smallest number is, other than it is a negative. Even if I am wrong, and a positive number CAN turn all 4 on, then if any negative number lights them all up, it would still be smaller than any possible option with positive numbers.