Question

Мальвина дала задание Буратино подобрать ключи к 10 запертым замкам. какой из 10 ключиков подходит к какому замку-неизвестно. За сколько попыток Буратино точно сможет определить от какого замка каждый ключ, если он старается сделать как можно меньше попыток?

Answer 1

К 1 замку ключ можно подобрать за 9 попыток, ко второму за 8 попыток, к третьему за 7 попыток, к четвертому за 6 попыток, к пятому за 5 попыток, к шестому за 4 попытки, к седьмому за 3 попытки, к восьмому за 2 попытки, к девятому за 1 попытку, а для десятого замка попыток не требуется, так как останется один ключ. С каждым следующим замком количество попыток уменьшается, так как уменьшаются и сами ключи (подобранные уже не будем брать в счет). Получается, что всего попыток: 9+8+7+6+5+4+3+2+1=45 попыток.
Ответ: 45 попыток

Answer 2

Task Analysis

To determine the minimum number of attempts Buratino needs to make in order to match each key to its corresponding lock, we can analyze the problem.

Key Points

- Number of Locks: There are 10 locks. - Number of Keys: Buratino has 10 keys. - Matching Process: Buratino needs to match each key to its corresponding lock through a trial-and-error process.

Solution Approach

To minimize the number of attempts, Buratino can use a systematic approach to match the keys with the locks. One efficient method is to use a binary search algorithm, which can help in identifying the correct lock for each key in the fewest number of attempts.

Binary Search Algorithm

The binary search algorithm is a divide-and-conquer algorithm that efficiently finds the position of a target value within a sorted array. In this case, the locks can be considered as a sorted array, and each key can be tested against the locks using the binary search approach.

Minimum Number of Attempts

Using the binary search algorithm, the minimum number of attempts required for Buratino to match each key to its corresponding lock can be calculated. The binary search algorithm has a time complexity of O(log n), where n is the number of elements in the array. Therefore, the minimum number of attempts can be calculated as log2(10), which equals 4.32. Since Buratino cannot make a fraction of an attempt, he would need to make 5 attempts to ensure he matches each key to its corresponding lock.

Conclusion

By employing the binary search algorithm, Buratino can determine the correct lock for each key in a minimum of 5 attempts, ensuring an efficient and systematic approach to the task.