Question

Перед нами 5 закрытых замков и 5 похожих ключей к ним. к каждому замку подходит только один ключ, но ключи смешались. возьмём один из замков, назовём его первым и попробуем открыть его каждым из пяти ключей. в лучшем случае он откроется первым же ключом, а в худшем - только пятым. сколько нужно в худшем случае произвести проб, чтобы открыть все замки

Answer 1

5*5=25......................................

Answer 2

Если ключей 5 и будем пробовать открыть каждый замок, а их тоже пять значит 5*5=25 проб

Answer 3

Problem Analysis

We have 5 closed locks and 5 keys that are mixed up. Each lock can be opened by only one key, and we want to find out how many attempts are needed in the worst-case scenario to open all the locks.

Solution

To find the worst-case scenario, we need to consider the situation where the key that opens a lock is the last key we try for that lock. This means that for each lock, we will try all the keys except the one that opens it before finally using the correct key.

Since we have 5 locks and 5 keys, we can assume that each lock has a unique key that opens it. Therefore, we will need to try all 5 keys for each lock before finding the correct one.

Calculation

To calculate the number of attempts needed in the worst-case scenario, we can multiply the number of locks by the number of keys minus 1 (since we don't count the correct key in the attempts).

Number of attempts = Number of locks * (Number of keys - 1)

Number of attempts = 5 * (5 - 1)

Number of attempts = 5 * 4

Number of attempts = 20

Therefore, in the worst-case scenario, we would need to make 20 attempts to open all the locks.

Answer: 20

Example

Let's go through an example to illustrate the solution. Suppose we have the following locks and keys:

Locks: A, B, C, D, E Keys: 1, 2, 3, 4, 5

In the worst-case scenario, we would need to try all the keys for each lock before finding the correct one. Here's how the attempts would look like:

1. Try key 1 for lock A (incorrect) 2. Try key 2 for lock A (incorrect) 3. Try key 3 for lock A (incorrect) 4. Try key 4 for lock A (incorrect) 5. Try key 5 for lock A (correct)

6. Try key 1 for lock B (incorrect) 7. Try key 2 for lock B (incorrect) 8. Try key 3 for lock B (incorrect) 9. Try key 4 for lock B (incorrect) 10. Try key 5 for lock B (correct)

11. Try key 1 for lock C (incorrect) 12. Try key 2 for lock C (incorrect) 13. Try key 3 for lock C (incorrect) 14. Try key 4 for lock C (incorrect) 15. Try key 5 for lock C (correct)

16. Try key 1 for lock D (incorrect) 17. Try key 2 for lock D (incorrect) 18. Try key 3 for lock D (incorrect) 19. Try key 4 for lock D (incorrect) 20. Try key 5 for lock D (correct)

In this example, we needed to make 20 attempts to open all the locks.

Conclusion

In the worst-case scenario, we would need to make 20 attempts to open all the locks.