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Can you crack the combination lock?

The sequence 11221 contains all 2-digit combinations using the numbers 1 and 2. Can you find a sequence that contains all the 3-digit combinations using the numbers 1, 2, and 3. What is the shortest such sequence? Can you find a sequence that contains all the 4-digit combinations using the numbers 1, 2, 3, and 4. What is the shortest such sequence? Then, can you break this lock? By which I mean, find the shortest sequence containing all 4-digit combinations using the numbers 0 to 9. The sequence is 10003 digits long (yes I misspoke in the video!)
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