163220

It states that each light has a rule so I worked logically through the first ten numbers making a record of which lights turn on for each number.

I quickly realised that green was even numbers. I then noticed that Blue came on for square numbers, and that yellow lit for triangle numbers. The red light came on for numbers ending in 1 or 6 (multiples of 5 starting at 1). Once I knew the four rules, I had to find a square number that ended in 6 and check that it was also a triangle number which meant that the answer was 36.