This month we have yet another great Martin Gardner puzzle. Full disclosure, doing this one made me a little dizzy! But if you do it in a “systematic” way, it’s possible to do it without getting nauseous!
One of these spirals is formed with a single piece of rope that has its ends joined. The other spiral is formed with two separate pieces of rope, each with joined ends.
Can you tell which is which by using only your eyes? No fair tracing the lines with your finger or cursor!
Answer:
One way to tackle this one is to “count” how many lines from the outside you are at as you start to trace in. For example, for the spiral on the left, starting at the top and moving left, as you come around the first turn, the line you are tracing is the second line from the top. As that line nears the center, it’s the 4th line from the bottom. And as you exit the center and head back up, that line is now the 3rd from the top. Moving systematically in this way and “keeping track” of which line you are on helps.
A similar skill can be helpful on the GMAT, GRE, SAT, and ACT. Some questions just require you to count or list or keep track of things as you work through the problem. Doing so systematically often helps a lot! For example, see this official GMAT question. There is a way to do this with a formula, but there’s also a way to “list” out the options in a systematic way that is pretty quick and that allows you to extrapolate the number of arrangements without counting out every single one! Give it a try!