The diagram below shows two identical, large squares divided into smaller squares.

Which area is larger, blue or green?

There is exactly one ladybug in each cell of a \(5\times 5\) square, as shown in the figure. Then, each ladybug simultaneously flies into a randomly selected, adjacent square that shares an edge.

Is it possible that, after all the ladybugs have moved, there is still only one ladybug in each cell?

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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