Brainteasers

Door Password

The password to open a door consists of 7 digits, no two of which are the same. So 0123456 is a possible password for example, but 0123455 is not. The door will open if you type in a 7 digit number, consisting of 7 different digits, and at least one of the digits matches its position in the password. For example, if the password is 0123456, the door will open if you type 0234567, because both your number and the password have 0 in the first position. What is the smallest number of attempts you must make to guarantee the door will open?

 
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