# A strange traffic light

I saw a mysterious picture on an electronic whiteboard in a school I was walking past. I couldn't hear what the teacher was saying, but I could see on the timetable that it said 'Maths'. Can you work out what the lesson was about?

• You gotta cut it out, man! I came back to Puzzling for wordplay puzzles, not this math mumbo-jumbo that my brain can't properly parse. :) – Bailey M Jan 21 '17 at 2:23
• Sorry @BaileyM ;( I hope you'll find something else - there were quite a few riddles posted yesterday UTC if they interest you... – boboquack Jan 21 '17 at 2:24
• Heh. I'm mostly kidding - though I really don't understand these math puzzles, I do enjoy seeing other, smarter people solve them! – Bailey M Jan 21 '17 at 2:27

## 1 Answer

I believe this is the rearrangement inequality, perhaps with coin values.

The rearrangement inequality is essentially saying that if you have two sets of positive numbers of the same size, and you pair one from each set with one from the other, take their products and sum, the greatest sum you can get is when you pair the greatest with the greatest, the least with the least, etc., and the lowest sum you can get is when you do the exact opposite.

Here, our sets are [2,3,5] and [20,50,100]. Green light represents the max, red light represents the min. The reason why the rest are yellow is because you can't work out how they are ordered without knowing the specific numbers in the sets.