There are eight locks and eight keys. Each lock can only be opened by its corresponding key. Inserting one key in a lock and turning it, constitutes an attempt. The minimum number of attempts required to ensure that all the locks are opened is
Question
There are eight locks and eight keys. Each lock can only be opened by its corresponding key. Inserting one key in a lock and turning it, constitutes an attempt. The minimum number of attempts required to ensure that all the locks are opened is
Solution
The minimum number of attempts required to ensure that all the locks are opened is 36. Here's the step-by-step process:
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Start with the first lock. You have 8 keys, so in the worst-case scenario, you might need to try all 8 keys before you find the one that works. That's 8 attempts.
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Move on to the second lock. Now you have 7 keys left (since you've already found the key for the first lock), so in the worst-case scenario, you might need to try all 7 keys before you find the one that works. That's 7 more attempts, for a total of 15 attempts so far.
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Continue this process. For the third lock, you'll have 6 keys left, so you might need 6 attempts. For the fourth lock, you'll have 5 keys left, so you might need 5 attempts. And so on.
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By the time you get to the eighth and final lock, you'll have just one key left, so you'll need only one attempt.
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Add up all the attempts: 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 attempts.
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