Peggy is a treasure hunter trying to open two treasure boxes. One box has 2 switches and the other has 4 switches. All of the switches are initially turned off. To open a treasure box,

- she must only change one switch at a time;
- she needs to register every possible combination exactly once.

Peggy successfully opens the box with 2 switches in the following manner:

Can Peggy open the box with 4 switches?

**Hint:** What if Peggy's box had 3 switches instead?

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