This is the kind of thing I really enjoy.
Nrich have also made a simpler version with only two lights and more guidance on how to understand and solve the patterns. That said, as the second version is explicit about how to represent the patterns algebraically, I suspect it is more likely to alienate or ‘freeze’ pupils who are perfectly able to identify and solve the patterns but have preconceptions about algebra and their abilities. I don’t think this is an error on the part of nrich – more a caveat when showing it to students.
I haven’t tried it in class yet – I’m trying to decide if it’s better for introducing or consolidating patterns/nth term, or just as a stand-alone piece for a one-off lesson.
PS – I was able to find a number when all four would light up, but only by trial and improvement (in the case below, only using multiples of 11n-3), not by setting it to equal zero. I’m not sure if I’m missing an obvious method, but I couldn’t get everything ‘to one side’ without new things popping up elsewhere! How should one go about solving an ‘equation’ such as this for one value of n:
8n-6 = 11n-3 = 3n-1 = 6n-4 ?
UPDATE: I’ve realised they can’t all have the same value of n when they’re solved, as it’s the number generated (74, in this case), not the number of the term (10, 7, 25, and 13, respectively), that they have in common. I’m flummoxed now!