A locker requires 3 numbers to unlock, every new number can be regenated by rolling the number current number down. And this locker is immidiately unlocked whenever you regenate right number without a confirm button.

If you start to unlock this by every single number from 000 to 999, what is the maximum time you have to regenate number to know the correct number?

The answer is 998.

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From 000 to 999 we have 10×10×10=1000 numbers (include 000 and 999) Because it's unlocked automatically whenever you regenate a correct number, so must be the initiate number is in correct, so one in 999 number left is correct. When you regenate 998 in 999 number left without true, so the last number left must be the correct number. So we don't have to regenate it to know.