Can you crack the combination lock?

Duration: 2 mins 53 secs
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Description: 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!)
 
Created: 2011-12-16 01:53
Collection: Quite Easily Done
Publisher: University of Cambridge
Copyright: Dr J.R. Grime
Language: eng (English)
Distribution: World     (downloadable)
Keywords: maths; math; mathematics; problem; puzzle; combination; lock; break; crack; sequence; combinatorics;
Categories: iTunes - Mathematics
Explicit content: No
Aspect Ratio: 16:9
Screencast: No
Bumper: UCS Default
Trailer: UCS Default
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