Strips of colored paper are made into loops and are chained to each other as shown above. The color pattern begins with the first loop and proceeds from left to right as red, blue, green, green, yellow, purple. This pattern is repeated for a chain of 96 loops. If the first few loops of the chain are removed so that the new beginning loop is no longer red and the new 16th loop is blue, what color will the new 51st loop in the chain be?

This is a classic example of a question writer getting carried away and taking things a step or two too far (not to say I am never guilty of this, of course).

First, let’s just take away all the rings before that blue one we know about. So let’s say the new new 1st ring is blue, making the old new 51st ring really the new new 36th ring. That also makes the new pattern we’re dealing with no longer start with red, but rather go thusly:

B, G, G, Y, P, R,
B, G, G, Y, P, R,
…

There are 6 colors in the pattern, so every 6th ring will be red. 36 is a multiple of 6, so the ring we’re asked about will be a red one.

(Read up more on repeating patterns.)