Question

Имеется пять одинаковых коробочек. В некоторых из них находятся золотые монеты (по одной в каждой коробочке), остальные пусты. На каждой из коробочек написано некоторое утверждение. Номер коробочки Надпись 1 Все коробки пусты 2 Здесь нет ничего и в коробках N3 и N5 - тоже. 3 Табличка N2 говорит правду 4 В коробках 2, 3 и 4 находятся монеты 5 Монеты находятся не менее, чем в двух коробочках Известно, что две надписи лгут, три оставшиеся - правдивы. Выясните, в каких коробках находятся монеты. В ответе укажите общее количество монет.

Answer 1

Монеты находятся в 2 коробочках в 1 и 4 .Всего 2 монеты

Answer 2

Problem Analysis

We have five identical boxes, each containing either a gold coin or nothing. Each box has a statement written on it. We need to determine which boxes contain the gold coins based on the given statements.

Given Information

- Box 1: "All boxes are empty." - Box 2: "There is nothing here, and there are no coins in boxes N3 and N5 either." - Box 3: "The label on Box N2 is telling the truth." - Box 4: "Coins are in boxes 2, 3, and 4." - Box 5: "There are at least two boxes with coins."

Solution

Let's analyze each statement and use logical reasoning to determine which boxes contain the gold coins.

1. Box 1: "All boxes are empty." - If this statement is true, then there are no gold coins in any of the boxes. - However, if this statement is false, then there must be at least one box with a gold coin.

2. Box 2: "There is nothing here, and there are no coins in boxes N3 and N5 either." - If this statement is true, then there are no gold coins in boxes 2, 3, or 5. - If this statement is false, then there must be a gold coin in box 2.

3. Box 3: "The label on Box N2 is telling the truth." - If this statement is true, then the statement on box 2 is true, which means there are no gold coins in boxes 2, 3, or 5. - If this statement is false, then the statement on box 2 is false, which means there is a gold coin in box 2.

4. Box 4: "Coins are in boxes 2, 3, and 4." - If this statement is true, then there are gold coins in boxes 2, 3, and 4. - If this statement is false, then there are no gold coins in boxes 2, 3, or 4.

5. Box 5: "There are at least two boxes with coins." - If this statement is true, then there are gold coins in at least two boxes. - If this statement is false, then there is at most one box with a gold coin.

Based on the above analysis, let's evaluate each statement:

- Box 1: If this statement is true, then there are no gold coins in any of the boxes. However, if this statement is false, then there must be at least one box with a gold coin. Therefore, this statement is false.

- Box 2: If this statement is true, then there are no gold coins in boxes 2, 3, or 5. If this statement is false, then there must be a gold coin in box 2. Since we know that statement 1 is false, there must be at least one gold coin. Therefore, this statement is false.

- Box 3: If this statement is true, then the statement on box 2 is true, which means there are no gold coins in boxes 2, 3, or 5. If this statement is false, then the statement on box 2 is false, which means there is a gold coin in box 2. Since we know that statement 2 is false, there must be a gold coin in box 2. Therefore, this statement is true.

- Box 4: If this statement is true, then there are gold coins in boxes 2, 3, and 4. If this statement is false, then there are no gold coins in boxes 2, 3, or 4. Since we know that statement 3 is true, there is a gold coin in box 2. Therefore, this statement is false. Therefore, this statement is false.

- Box 5: If this statement is true, then there are gold coins in at least two boxes. If this statement is false, then there is at most one box with a gold coin. Since we know that statement 4 is false, there are no gold coins in boxes 2, 3, or 4. Therefore, there is at most one box with a gold coin. Therefore, this statement is false.

Based on the analysis, we can conclude that: - Box 1 is false, so it contains a gold coin. - Box 2 is false, so it contains a gold coin. - Box 3 is true, so it does not contain a gold coin. - Box 4 is false, so it does not contain a gold coin. - Box 5 is false, so it does not contain a gold coin.

Therefore, the gold coins are in boxes 1 and 2. The total number of gold coins is 2.

Answer

The gold coins are in boxes 1 and 2, and the total number of gold coins is 2.