It is known that in a code lock, only the buttons with numbers 1, 2, and 3 are functional, and the code for this lock is three digits long and does not contain any other digits. Write the shortest sequence of digits that will definitely open this lock (the lock opens as soon as the correct three digits are pressed in the right order).

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There are $3^{3}=27$ different three-digit numbers, in the notation of which the digits 1, 2, 3 are used. Besides the first two digits in the sequence of button presses, each of the other digits serves as the last digit of some three-digit number. Therefore, the required sequence must contain no fewer than $27+2=29$ digits. Twenty-nine digits are already sufficient to open the lock; for example, the sequence 11123222133313121223113233211 will do.