A concave polygon can be equilateral. For example, the concave octagon to the right is equilateral.

What is the **least** number of sides a concave equilateral polygon can have?

One day, Alice, Betty, Cathy, David, and Edward were at home playing hide and seek. Unfortunately, one of them accidentally collided into a flower vase. When their mother came back home and saw the broken vase, she asked them who did it.

**Alice:** "Betty broke it!"

**Betty:** "Alice is not telling the truth."

**Cathy:** "I did it!"

**David:** "I did not break it and Betty is lying!"

**Edward:** "David is telling the truth!"

Given that **at least three** children are telling the truth, who broke the vase?

A *catalyst* is a molecule that can increase the rate of a chemical reaction.

Suppose we have a reaction that releases energy \(E.\) If we introduce a catalyst into the reaction and assume that no other conditions change, does the amount of energy released during any given reaction increase, decrease, or stay the same?

You are given a set of cards arranged in a line. Each card is either \(\color{black}{\text{black}}\) or \(\color{red}{\text{red}}\). You may divide the cards into two parts by picking a line before or after the whole cards (so that a part can contain 0 cards), or somewhere between two cards.

No matter how many cards are arranged in whatever manner, can you always ensure the number of \(\color{black}{\text{black}}\) cards in the left part is exactly the same as the number of \(\color{red}{\text{red}}\) cards in the right part?

An example split that fulfills the condition is shown below.

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