# 3. Clone 1

On an island, there live knights who always tell the truth, and liars who always lie. Before a friendly match, 30 islanders gathered in T-shirts with numbers on them—arbitrary natural numbers. Each of them said: “I have a T-shirt with an odd number.” After that, they exchanged T-shirts, and each said: “I have a T-shirt with an even number.” How many knights participated in the exchange?
# Answer: 15

## Solution

Notice that each knight exchanged a shirt with an odd number for a shirt with an even number, while each liar exchanged a shirt with an even number for a shirt with an odd number. This means that each knight exchanged with a liar, so there are no more knights than liars. On the other hand, each liar exchanged with a knight, so there are no more liars than knights. Therefore, the number of knights and liars is the same - half of the total number of islanders.

## Clone 2

On an island, there live knights who always tell the truth and liars who always lie. Before a friendly match, 40 islanders gathered in shirts with numbers - arbitrary natural numbers. Each of them said: "I have a shirt with an odd number." After this, they exchanged shirts, and each said: "I have a shirt with an even number." How many knights participated in the exchange?

## Answer: 20

## Clone 3

On an island, there live knights who always tell the truth and liars who always lie. Before a friendly match, 50 islanders gathered in shirts with numbers - arbitrary natural numbers. Each of them said: "I have a shirt with an odd number." After this, they exchanged shirts, and each said: "I have a shirt with an even number." How many knights participated in the exchange?

## Answer: 25

## Clone 4

On an island, there live knights who always tell the truth and liars who always lie. Before a friendly match, 60 islanders gathered in shirts with numbers - natural numbers. Each of them said: "I have a shirt with an odd number." After this, they exchanged shirts, and each said: "I have a shirt with an even number." How many knights participated in the exchange?

## Answer: 30

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