To print out a copy of these instructions, click below:

If you like these puzzles,
you might also like...

When most people think of waves, such as ocean waves, they imagine simple, regular wave motion. But waves can take on much more complicated shapes and patterns. First, simple waves can be manipulated by stretching, compressing, and shifting. Multiple simple waves can then be added together to form new waves that are complicated but still regular and repeating. These complicated waves are called "Fourier series", named after Joseph Fourier (1768-1830) who studied heat conduction.

In the following puzzles, a simple wave will be manipulated using stretchers, compressors, and shifters. Given the choices of wave manipulators, you need to determine which combination will produce the wave given. Here are some examples of wave manipulators:

Using combinations of these wave manipulators, we can produce complicated waves. In this example, a simple wave that is compressed by 2 and then shifted by 3 is combined with another simple wave that is compressed by 3 and then shifted by 2 to form the complicated wave shown.

When two waves are added together, they typically produce waves within the wave. In other words, there is typically some large-scale behavior and some small-scale behavior layered on top of it. Determining these two components may help you figure out which two waves were added together.