[Guest]

My friend called me with another math puzzle:

You know the Ford Doors with the number pad locks?

I've seen them on Fusions and Taurus SHOs...

They have five keys with the 10 digits paired as such:

[1-2] [3-4] [5-6] [7-8] [9-0]

My friend wondered, how could we quickest hack the lock of a random, unknown code if we know that the code is 5 digits long?

The 5 digit codes can run together, so when you type

[1] [1] [1] [1] [1]

you've tested one code

but when you type

[1] [1] [1] [1] [1] [2]

you've tested two codes:

[1] [1] [1] [1] [1] and [1] [1] [1] [1] [2]

[Guest]

In other words, what is the shortest sequence of code-guesses?

[superprismatic]

10,000 -- A de Bruijn sequence denoted B(10,5) has 10,004 individual numbers (from 0 to 9) comprising all 10,000 possible sequences of quintuplets of digits precisely once each and chained together with an overlap of 4 for each link of the chain.

Edited March 24, 2010 by superprismatic

[plainglazed]

there are 3129 keys to punch to ensure access. 5⁵+4? seems to me that 13579 and 23579 are the same so look at the five keys as single digits 1-5. even if this much is right, can't quite visualize if you can line up all 3125 possibilities one after another sharing four numbers. think since there is an even distribution of each key it should be doable.

[plainglazed]

did some wiki research re superprismatic's de Bruijn sequence and would now say 3125 keys to punch. here's one solution labeling [1-2]0, [3-4]=1, [5-6]=2, [7-8]=3, [9-0]=4. if I understand the wiki article correctly there are (5!⁵⁴/5⁵)-1 other possibilities (is that right superprismatic, yikes!):

0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 1 1 0 0 0 1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 2 1 0 0 0 2 2 0 0 0 2 3 0 0 0 2 4 0 0 0 3 1 0 0 0 3 2 0 0 0 3 3 0 0 0 3 4 0 0 0 4 1 0 0 0 4 2 0 0 0 4 3 0 0 0 4 4 0 0 1 0 1 0 0 1 0 2 0 0 1 0 3 0 0 1 0 4 0 0 1 1 1 0 0 1 1 2 0 0 1 1 3 0 0 1 1 4 0 0 1 2 1 0 0 1 2 2 0 0 1 2 3 0 0 1 2 4 0 0 1 3 1 0 0 1 3 2 0 0 1 3 3 0 0 1 3 4 0 0 1 4 1 0 0 1 4 2 0 0 1 4 3 0 0 1 4 4 0 0 2 0 1 0 0 2 0 2 0 0 2 0 3 0 0 2 0 4 0 0 2 1 1 0 0 2 1 2 0 0 2 1 3 0 0 2 1 4 0 0 2 2 1 0 0 2 2 2 0 0 2 2 3 0 0 2 2 4 0 0 2 3 1 0 0 2 3 2 0 0 2 3 3 0 0 2 3 4 0 0 2 4 1 0 0 2 4 2 0 0 2 4 3 0 0 2 4 4 0 0 3 0 1 0 0 3 0 2 0 0 3 0 3 0 0 3 0 4 0 0 3 1 1 0 0 3 1 2 0 0 3 1 3 0 0 3 1 4 0 0 3 2 1 0 0 3 2 2 0 0 3 2 3 0 0 3 2 4 0 0 3 3 1 0 0 3 3 2 0 0 3 3 3 0 0 3 3 4 0 0 3 4 1 0 0 3 4 2 0 0 3 4 3 0 0 3 4 4 0 0 4 0 1 0 0 4 0 2 0 0 4 0 3 0 0 4 0 4 0 0 4 1 1 0 0 4 1 2 0 0 4 1 3 0 0 4 1 4 0 0 4 2 1 0 0 4 2 2 0 0 4 2 3 0 0 4 2 4 0 0 4 3 1 0 0 4 3 2 0 0 4 3 3 0 0 4 3 4 0 0 4 4 1 0 0 4 4 2 0 0 4 4 3 0 0 4 4 4 0 1 0 1 1 0 1 0 1 2 0 1 0 1 3 0 1 0 1 4 0 1 0 2 1 0 1 0 2 2 0 1 0 2 3 0 1 0 2 4 0 1 0 3 1 0 1 0 3 2 0 1 0 3 3 0 1 0 3 4 0 1 0 4 1 0 1 0 4 2 0 1 0 4 3 0 1 0 4 4 0 1 1 0 2 0 1 1 0 3 0 1 1 0 4 0 1 1 1 1 0 1 1 1 2 0 1 1 1 3 0 1 1 1 4 0 1 1 2 1 0 1 1 2 2 0 1 1 2 3 0 1 1 2 4 0 1 1 3 1 0 1 1 3 2 0 1 1 3 3 0 1 1 3 4 0 1 1 4 1 0 1 1 4 2 0 1 1 4 3 0 1 1 4 4 0 1 2 0 2 0 1 2 0 3 0 1 2 0 4 0 1 2 1 1 0 1 2 1 2 0 1 2 1 3 0 1 2 1 4 0 1 2 2 1 0 1 2 2 2 0 1 2 2 3 0 1 2 2 4 0 1 2 3 1 0 1 2 3 2 0 1 2 3 3 0 1 2 3 4 0 1 2 4 1 0 1 2 4 2 0 1 2 4 3 0 1 2 4 4 0 1 3 0 2 0 1 3 0 3 0 1 3 0 4 0 1 3 1 1 0 1 3 1 2 0 1 3 1 3 0 1 3 1 4 0 1 3 2 1 0 1 3 2 2 0 1 3 2 3 0 1 3 2 4 0 1 3 3 1 0 1 3 3 2 0 1 3 3 3 0 1 3 3 4 0 1 3 4 1 0 1 3 4 2 0 1 3 4 3 0 1 3 4 4 0 1 4 0 2 0 1 4 0 3 0 1 4 0 4 0 1 4 1 1 0 1 4 1 2 0 1 4 1 3 0 1 4 1 4 0 1 4 2 1 0 1 4 2 2 0 1 4 2 3 0 1 4 2 4 0 1 4 3 1 0 1 4 3 2 0 1 4 3 3 0 1 4 3 4 0 1 4 4 1 0 1 4 4 2 0 1 4 4 3 0 1 4 4 4 0 2 0 2 1 0 2 0 2 2 0 2 0 2 3 0 2 0 2 4 0 2 0 3 1 0 2 0 3 2 0 2 0 3 3 0 2 0 3 4 0 2 0 4 1 0 2 0 4 2 0 2 0 4 3 0 2 0 4 4 0 2 1 0 3 0 2 1 0 4 0 2 1 1 1 0 2 1 1 2 0 2 1 1 3 0 2 1 1 4 0 2 1 2 1 0 2 1 2 2 0 2 1 2 3 0 2 1 2 4 0 2 1 3 1 0 2 1 3 2 0 2 1 3 3 0 2 1 3 4 0 2 1 4 1 0 2 1 4 2 0 2 1 4 3 0 2 1 4 4 0 2 2 0 3 0 2 2 0 4 0 2 2 1 1 0 2 2 1 2 0 2 2 1 3 0 2 2 1 4 0 2 2 2 1 0 2 2 2 2 0 2 2 2 3 0 2 2 2 4 0 2 2 3 1 0 2 2 3 2 0 2 2 3 3 0 2 2 3 4 0 2 2 4 1 0 2 2 4 2 0 2 2 4 3 0 2 2 4 4 0 2 3 0 3 0 2 3 0 4 0 2 3 1 1 0 2 3 1 2 0 2 3 1 3 0 2 3 1 4 0 2 3 2 1 0 2 3 2 2 0 2 3 2 3 0 2 3 2 4 0 2 3 3 1 0 2 3 3 2 0 2 3 3 3 0 2 3 3 4 0 2 3 4 1 0 2 3 4 2 0 2 3 4 3 0 2 3 4 4 0 2 4 0 3 0 2 4 0 4 0 2 4 1 1 0 2 4 1 2 0 2 4 1 3 0 2 4 1 4 0 2 4 2 1 0 2 4 2 2 0 2 4 2 3 0 2 4 2 4 0 2 4 3 1 0 2 4 3 2 0 2 4 3 3 0 2 4 3 4 0 2 4 4 1 0 2 4 4 2 0 2 4 4 3 0 2 4 4 4 0 3 0 3 1 0 3 0 3 2 0 3 0 3 3 0 3 0 3 4 0 3 0 4 1 0 3 0 4 2 0 3 0 4 3 0 3 0 4 4 0 3 1 0 4 0 3 1 1 1 0 3 1 1 2 0 3 1 1 3 0 3 1 1 4 0 3 1 2 1 0 3 1 2 2 0 3 1 2 3 0 3 1 2 4 0 3 1 3 1 0 3 1 3 2 0 3 1 3 3 0 3 1 3 4 0 3 1 4 1 0 3 1 4 2 0 3 1 4 3 0 3 1 4 4 0 3 2 0 4 0 3 2 1 1 0 3 2 1 2 0 3 2 1 3 0 3 2 1 4 0 3 2 2 1 0 3 2 2 2 0 3 2 2 3 0 3 2 2 4 0 3 2 3 1 0 3 2 3 2 0 3 2 3 3 0 3 2 3 4 0 3 2 4 1 0 3 2 4 2 0 3 2 4 3 0 3 2 4 4 0 3 3 0 4 0 3 3 1 1 0 3 3 1 2 0 3 3 1 3 0 3 3 1 4 0 3 3 2 1 0 3 3 2 2 0 3 3 2 3 0 3 3 2 4 0 3 3 3 1 0 3 3 3 2 0 3 3 3 3 0 3 3 3 4 0 3 3 4 1 0 3 3 4 2 0 3 3 4 3 0 3 3 4 4 0 3 4 0 4 0 3 4 1 1 0 3 4 1 2 0 3 4 1 3 0 3 4 1 4 0 3 4 2 1 0 3 4 2 2 0 3 4 2 3 0 3 4 2 4 0 3 4 3 1 0 3 4 3 2 0 3 4 3 3 0 3 4 3 4 0 3 4 4 1 0 3 4 4 2 0 3 4 4 3 0 3 4 4 4 0 4 0 4 1 0 4 0 4 2 0 4 0 4 3 0 4 0 4 4 0 4 1 1 1 0 4 1 1 2 0 4 1 1 3 0 4 1 1 4 0 4 1 2 1 0 4 1 2 2 0 4 1 2 3 0 4 1 2 4 0 4 1 3 1 0 4 1 3 2 0 4 1 3 3 0 4 1 3 4 0 4 1 4 1 0 4 1 4 2 0 4 1 4 3 0 4 1 4 4 0 4 2 1 1 0 4 2 1 2 0 4 2 1 3 0 4 2 1 4 0 4 2 2 1 0 4 2 2 2 0 4 2 2 3 0 4 2 2 4 0 4 2 3 1 0 4 2 3 2 0 4 2 3 3 0 4 2 3 4 0 4 2 4 1 0 4 2 4 2 0 4 2 4 3 0 4 2 4 4 0 4 3 1 1 0 4 3 1 2 0 4 3 1 3 0 4 3 1 4 0 4 3 2 1 0 4 3 2 2 0 4 3 2 3 0 4 3 2 4 0 4 3 3 1 0 4 3 3 2 0 4 3 3 3 0 4 3 3 4 0 4 3 4 1 0 4 3 4 2 0 4 3 4 3 0 4 3 4 4 0 4 4 1 1 0 4 4 1 2 0 4 4 1 3 0 4 4 1 4 0 4 4 2 1 0 4 4 2 2 0 4 4 2 3 0 4 4 2 4 0 4 4 3 1 0 4 4 3 2 0 4 4 3 3 0 4 4 3 4 0 4 4 4 1 0 4 4 4 2 0 4 4 4 3 0 4 4 4 4 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 4 1 1 1 2 2 1 1 1 2 3 1 1 1 2 4 1 1 1 3 2 1 1 1 3 3 1 1 1 3 4 1 1 1 4 2 1 1 1 4 3 1 1 1 4 4 1 1 2 1 2 1 1 2 1 3 1 1 2 1 4 1 1 2 2 2 1 1 2 2 3 1 1 2 2 4 1 1 2 3 2 1 1 2 3 3 1 1 2 3 4 1 1 2 4 2 1 1 2 4 3 1 1 2 4 4 1 1 3 1 2 1 1 3 1 3 1 1 3 1 4 1 1 3 2 2 1 1 3 2 3 1 1 3 2 4 1 1 3 3 2 1 1 3 3 3 1 1 3 3 4 1 1 3 4 2 1 1 3 4 3 1 1 3 4 4 1 1 4 1 2 1 1 4 1 3 1 1 4 1 4 1 1 4 2 2 1 1 4 2 3 1 1 4 2 4 1 1 4 3 2 1 1 4 3 3 1 1 4 3 4 1 1 4 4 2 1 1 4 4 3 1 1 4 4 4 1 2 1 2 2 1 2 1 2 3 1 2 1 2 4 1 2 1 3 2 1 2 1 3 3 1 2 1 3 4 1 2 1 4 2 1 2 1 4 3 1 2 1 4 4 1 2 2 1 3 1 2 2 1 4 1 2 2 2 2 1 2 2 2 3 1 2 2 2 4 1 2 2 3 2 1 2 2 3 3 1 2 2 3 4 1 2 2 4 2 1 2 2 4 3 1 2 2 4 4 1 2 3 1 3 1 2 3 1 4 1 2 3 2 2 1 2 3 2 3 1 2 3 2 4 1 2 3 3 2 1 2 3 3 3 1 2 3 3 4 1 2 3 4 2 1 2 3 4 3 1 2 3 4 4 1 2 4 1 3 1 2 4 1 4 1 2 4 2 2 1 2 4 2 3 1 2 4 2 4 1 2 4 3 2 1 2 4 3 3 1 2 4 3 4 1 2 4 4 2 1 2 4 4 3 1 2 4 4 4 1 3 1 3 2 1 3 1 3 3 1 3 1 3 4 1 3 1 4 2 1 3 1 4 3 1 3 1 4 4 1 3 2 1 4 1 3 2 2 2 1 3 2 2 3 1 3 2 2 4 1 3 2 3 2 1 3 2 3 3 1 3 2 3 4 1 3 2 4 2 1 3 2 4 3 1 3 2 4 4 1 3 3 1 4 1 3 3 2 2 1 3 3 2 3 1 3 3 2 4 1 3 3 3 2 1 3 3 3 3 1 3 3 3 4 1 3 3 4 2 1 3 3 4 3 1 3 3 4 4 1 3 4 1 4 1 3 4 2 2 1 3 4 2 3 1 3 4 2 4 1 3 4 3 2 1 3 4 3 3 1 3 4 3 4 1 3 4 4 2 1 3 4 4 3 1 3 4 4 4 1 4 1 4 2 1 4 1 4 3 1 4 1 4 4 1 4 2 2 2 1 4 2 2 3 1 4 2 2 4 1 4 2 3 2 1 4 2 3 3 1 4 2 3 4 1 4 2 4 2 1 4 2 4 3 1 4 2 4 4 1 4 3 2 2 1 4 3 2 3 1 4 3 2 4 1 4 3 3 2 1 4 3 3 3 1 4 3 3 4 1 4 3 4 2 1 4 3 4 3 1 4 3 4 4 1 4 4 2 2 1 4 4 2 3 1 4 4 2 4 1 4 4 3 2 1 4 4 3 3 1 4 4 3 4 1 4 4 4 2 1 4 4 4 3 1 4 4 4 4 2 2 2 2 2 3 2 2 2 2 4 2 2 2 3 3 2 2 2 3 4 2 2 2 4 3 2 2 2 4 4 2 2 3 2 3 2 2 3 2 4 2 2 3 3 3 2 2 3 3 4 2 2 3 4 3 2 2 3 4 4 2 2 4 2 3 2 2 4 2 4 2 2 4 3 3 2 2 4 3 4 2 2 4 4 3 2 2 4 4 4 2 3 2 3 3 2 3 2 3 4 2 3 2 4 3 2 3 2 4 4 2 3 3 2 4 2 3 3 3 3 2 3 3 3 4 2 3 3 4 3 2 3 3 4 4 2 3 4 2 4 2 3 4 3 3 2 3 4 3 4 2 3 4 4 3 2 3 4 4 4 2 4 2 4 3 2 4 2 4 4 2 4 3 3 3 2 4 3 3 4 2 4 3 4 3 2 4 3 4 4 2 4 4 3 3 2 4 4 3 4 2 4 4 4 3 2 4 4 4 4 3 3 3 3 3 4 3 3 3 4 4 3 3 4 3 4 3 3 4 4 4 3 4 3 4 4 3 4 4 4 4 4

Good luck, but if you get caught, you didn't get it from me.

[superprismatic]

did some wiki research re superprismatic's de Bruijn sequence and would now say 3125 keys to punch. here's one solution labeling [1-2]0, [3-4]=1, [5-6]=2, [7-8]=3, [9-0]=4. if I understand the wiki article correctly there are (5!⁵⁴/5⁵)-1 other possibilities (is that right superprismatic, yikes!):

0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 1 1 0 0 0 1 2 0 0 0 1 3 0 0 0 1 4 0 0 0 2 1 0 0 0 2 2 0 0 0 2 3 0 0 0 2 4 0 0 0 3 1 0 0 0 3 2 0 0 0 3 3 0 0 0 3 4 0 0 0 4 1 0 0 0 4 2 0 0 0 4 3 0 0 0 4 4 0 0 1 0 1 0 0 1 0 2 0 0 1 0 3 0 0 1 0 4 0 0 1 1 1 0 0 1 1 2 0 0 1 1 3 0 0 1 1 4 0 0 1 2 1 0 0 1 2 2 0 0 1 2 3 0 0 1 2 4 0 0 1 3 1 0 0 1 3 2 0 0 1 3 3 0 0 1 3 4 0 0 1 4 1 0 0 1 4 2 0 0 1 4 3 0 0 1 4 4 0 0 2 0 1 0 0 2 0 2 0 0 2 0 3 0 0 2 0 4 0 0 2 1 1 0 0 2 1 2 0 0 2 1 3 0 0 2 1 4 0 0 2 2 1 0 0 2 2 2 0 0 2 2 3 0 0 2 2 4 0 0 2 3 1 0 0 2 3 2 0 0 2 3 3 0 0 2 3 4 0 0 2 4 1 0 0 2 4 2 0 0 2 4 3 0 0 2 4 4 0 0 3 0 1 0 0 3 0 2 0 0 3 0 3 0 0 3 0 4 0 0 3 1 1 0 0 3 1 2 0 0 3 1 3 0 0 3 1 4 0 0 3 2 1 0 0 3 2 2 0 0 3 2 3 0 0 3 2 4 0 0 3 3 1 0 0 3 3 2 0 0 3 3 3 0 0 3 3 4 0 0 3 4 1 0 0 3 4 2 0 0 3 4 3 0 0 3 4 4 0 0 4 0 1 0 0 4 0 2 0 0 4 0 3 0 0 4 0 4 0 0 4 1 1 0 0 4 1 2 0 0 4 1 3 0 0 4 1 4 0 0 4 2 1 0 0 4 2 2 0 0 4 2 3 0 0 4 2 4 0 0 4 3 1 0 0 4 3 2 0 0 4 3 3 0 0 4 3 4 0 0 4 4 1 0 0 4 4 2 0 0 4 4 3 0 0 4 4 4 0 1 0 1 1 0 1 0 1 2 0 1 0 1 3 0 1 0 1 4 0 1 0 2 1 0 1 0 2 2 0 1 0 2 3 0 1 0 2 4 0 1 0 3 1 0 1 0 3 2 0 1 0 3 3 0 1 0 3 4 0 1 0 4 1 0 1 0 4 2 0 1 0 4 3 0 1 0 4 4 0 1 1 0 2 0 1 1 0 3 0 1 1 0 4 0 1 1 1 1 0 1 1 1 2 0 1 1 1 3 0 1 1 1 4 0 1 1 2 1 0 1 1 2 2 0 1 1 2 3 0 1 1 2 4 0 1 1 3 1 0 1 1 3 2 0 1 1 3 3 0 1 1 3 4 0 1 1 4 1 0 1 1 4 2 0 1 1 4 3 0 1 1 4 4 0 1 2 0 2 0 1 2 0 3 0 1 2 0 4 0 1 2 1 1 0 1 2 1 2 0 1 2 1 3 0 1 2 1 4 0 1 2 2 1 0 1 2 2 2 0 1 2 2 3 0 1 2 2 4 0 1 2 3 1 0 1 2 3 2 0 1 2 3 3 0 1 2 3 4 0 1 2 4 1 0 1 2 4 2 0 1 2 4 3 0 1 2 4 4 0 1 3 0 2 0 1 3 0 3 0 1 3 0 4 0 1 3 1 1 0 1 3 1 2 0 1 3 1 3 0 1 3 1 4 0 1 3 2 1 0 1 3 2 2 0 1 3 2 3 0 1 3 2 4 0 1 3 3 1 0 1 3 3 2 0 1 3 3 3 0 1 3 3 4 0 1 3 4 1 0 1 3 4 2 0 1 3 4 3 0 1 3 4 4 0 1 4 0 2 0 1 4 0 3 0 1 4 0 4 0 1 4 1 1 0 1 4 1 2 0 1 4 1 3 0 1 4 1 4 0 1 4 2 1 0 1 4 2 2 0 1 4 2 3 0 1 4 2 4 0 1 4 3 1 0 1 4 3 2 0 1 4 3 3 0 1 4 3 4 0 1 4 4 1 0 1 4 4 2 0 1 4 4 3 0 1 4 4 4 0 2 0 2 1 0 2 0 2 2 0 2 0 2 3 0 2 0 2 4 0 2 0 3 1 0 2 0 3 2 0 2 0 3 3 0 2 0 3 4 0 2 0 4 1 0 2 0 4 2 0 2 0 4 3 0 2 0 4 4 0 2 1 0 3 0 2 1 0 4 0 2 1 1 1 0 2 1 1 2 0 2 1 1 3 0 2 1 1 4 0 2 1 2 1 0 2 1 2 2 0 2 1 2 3 0 2 1 2 4 0 2 1 3 1 0 2 1 3 2 0 2 1 3 3 0 2 1 3 4 0 2 1 4 1 0 2 1 4 2 0 2 1 4 3 0 2 1 4 4 0 2 2 0 3 0 2 2 0 4 0 2 2 1 1 0 2 2 1 2 0 2 2 1 3 0 2 2 1 4 0 2 2 2 1 0 2 2 2 2 0 2 2 2 3 0 2 2 2 4 0 2 2 3 1 0 2 2 3 2 0 2 2 3 3 0 2 2 3 4 0 2 2 4 1 0 2 2 4 2 0 2 2 4 3 0 2 2 4 4 0 2 3 0 3 0 2 3 0 4 0 2 3 1 1 0 2 3 1 2 0 2 3 1 3 0 2 3 1 4 0 2 3 2 1 0 2 3 2 2 0 2 3 2 3 0 2 3 2 4 0 2 3 3 1 0 2 3 3 2 0 2 3 3 3 0 2 3 3 4 0 2 3 4 1 0 2 3 4 2 0 2 3 4 3 0 2 3 4 4 0 2 4 0 3 0 2 4 0 4 0 2 4 1 1 0 2 4 1 2 0 2 4 1 3 0 2 4 1 4 0 2 4 2 1 0 2 4 2 2 0 2 4 2 3 0 2 4 2 4 0 2 4 3 1 0 2 4 3 2 0 2 4 3 3 0 2 4 3 4 0 2 4 4 1 0 2 4 4 2 0 2 4 4 3 0 2 4 4 4 0 3 0 3 1 0 3 0 3 2 0 3 0 3 3 0 3 0 3 4 0 3 0 4 1 0 3 0 4 2 0 3 0 4 3 0 3 0 4 4 0 3 1 0 4 0 3 1 1 1 0 3 1 1 2 0 3 1 1 3 0 3 1 1 4 0 3 1 2 1 0 3 1 2 2 0 3 1 2 3 0 3 1 2 4 0 3 1 3 1 0 3 1 3 2 0 3 1 3 3 0 3 1 3 4 0 3 1 4 1 0 3 1 4 2 0 3 1 4 3 0 3 1 4 4 0 3 2 0 4 0 3 2 1 1 0 3 2 1 2 0 3 2 1 3 0 3 2 1 4 0 3 2 2 1 0 3 2 2 2 0 3 2 2 3 0 3 2 2 4 0 3 2 3 1 0 3 2 3 2 0 3 2 3 3 0 3 2 3 4 0 3 2 4 1 0 3 2 4 2 0 3 2 4 3 0 3 2 4 4 0 3 3 0 4 0 3 3 1 1 0 3 3 1 2 0 3 3 1 3 0 3 3 1 4 0 3 3 2 1 0 3 3 2 2 0 3 3 2 3 0 3 3 2 4 0 3 3 3 1 0 3 3 3 2 0 3 3 3 3 0 3 3 3 4 0 3 3 4 1 0 3 3 4 2 0 3 3 4 3 0 3 3 4 4 0 3 4 0 4 0 3 4 1 1 0 3 4 1 2 0 3 4 1 3 0 3 4 1 4 0 3 4 2 1 0 3 4 2 2 0 3 4 2 3 0 3 4 2 4 0 3 4 3 1 0 3 4 3 2 0 3 4 3 3 0 3 4 3 4 0 3 4 4 1 0 3 4 4 2 0 3 4 4 3 0 3 4 4 4 0 4 0 4 1 0 4 0 4 2 0 4 0 4 3 0 4 0 4 4 0 4 1 1 1 0 4 1 1 2 0 4 1 1 3 0 4 1 1 4 0 4 1 2 1 0 4 1 2 2 0 4 1 2 3 0 4 1 2 4 0 4 1 3 1 0 4 1 3 2 0 4 1 3 3 0 4 1 3 4 0 4 1 4 1 0 4 1 4 2 0 4 1 4 3 0 4 1 4 4 0 4 2 1 1 0 4 2 1 2 0 4 2 1 3 0 4 2 1 4 0 4 2 2 1 0 4 2 2 2 0 4 2 2 3 0 4 2 2 4 0 4 2 3 1 0 4 2 3 2 0 4 2 3 3 0 4 2 3 4 0 4 2 4 1 0 4 2 4 2 0 4 2 4 3 0 4 2 4 4 0 4 3 1 1 0 4 3 1 2 0 4 3 1 3 0 4 3 1 4 0 4 3 2 1 0 4 3 2 2 0 4 3 2 3 0 4 3 2 4 0 4 3 3 1 0 4 3 3 2 0 4 3 3 3 0 4 3 3 4 0 4 3 4 1 0 4 3 4 2 0 4 3 4 3 0 4 3 4 4 0 4 4 1 1 0 4 4 1 2 0 4 4 1 3 0 4 4 1 4 0 4 4 2 1 0 4 4 2 2 0 4 4 2 3 0 4 4 2 4 0 4 4 3 1 0 4 4 3 2 0 4 4 3 3 0 4 4 3 4 0 4 4 4 1 0 4 4 4 2 0 4 4 4 3 0 4 4 4 4 1 1 1 1 1 2 1 1 1 1 3 1 1 1 1 4 1 1 1 2 2 1 1 1 2 3 1 1 1 2 4 1 1 1 3 2 1 1 1 3 3 1 1 1 3 4 1 1 1 4 2 1 1 1 4 3 1 1 1 4 4 1 1 2 1 2 1 1 2 1 3 1 1 2 1 4 1 1 2 2 2 1 1 2 2 3 1 1 2 2 4 1 1 2 3 2 1 1 2 3 3 1 1 2 3 4 1 1 2 4 2 1 1 2 4 3 1 1 2 4 4 1 1 3 1 2 1 1 3 1 3 1 1 3 1 4 1 1 3 2 2 1 1 3 2 3 1 1 3 2 4 1 1 3 3 2 1 1 3 3 3 1 1 3 3 4 1 1 3 4 2 1 1 3 4 3 1 1 3 4 4 1 1 4 1 2 1 1 4 1 3 1 1 4 1 4 1 1 4 2 2 1 1 4 2 3 1 1 4 2 4 1 1 4 3 2 1 1 4 3 3 1 1 4 3 4 1 1 4 4 2 1 1 4 4 3 1 1 4 4 4 1 2 1 2 2 1 2 1 2 3 1 2 1 2 4 1 2 1 3 2 1 2 1 3 3 1 2 1 3 4 1 2 1 4 2 1 2 1 4 3 1 2 1 4 4 1 2 2 1 3 1 2 2 1 4 1 2 2 2 2 1 2 2 2 3 1 2 2 2 4 1 2 2 3 2 1 2 2 3 3 1 2 2 3 4 1 2 2 4 2 1 2 2 4 3 1 2 2 4 4 1 2 3 1 3 1 2 3 1 4 1 2 3 2 2 1 2 3 2 3 1 2 3 2 4 1 2 3 3 2 1 2 3 3 3 1 2 3 3 4 1 2 3 4 2 1 2 3 4 3 1 2 3 4 4 1 2 4 1 3 1 2 4 1 4 1 2 4 2 2 1 2 4 2 3 1 2 4 2 4 1 2 4 3 2 1 2 4 3 3 1 2 4 3 4 1 2 4 4 2 1 2 4 4 3 1 2 4 4 4 1 3 1 3 2 1 3 1 3 3 1 3 1 3 4 1 3 1 4 2 1 3 1 4 3 1 3 1 4 4 1 3 2 1 4 1 3 2 2 2 1 3 2 2 3 1 3 2 2 4 1 3 2 3 2 1 3 2 3 3 1 3 2 3 4 1 3 2 4 2 1 3 2 4 3 1 3 2 4 4 1 3 3 1 4 1 3 3 2 2 1 3 3 2 3 1 3 3 2 4 1 3 3 3 2 1 3 3 3 3 1 3 3 3 4 1 3 3 4 2 1 3 3 4 3 1 3 3 4 4 1 3 4 1 4 1 3 4 2 2 1 3 4 2 3 1 3 4 2 4 1 3 4 3 2 1 3 4 3 3 1 3 4 3 4 1 3 4 4 2 1 3 4 4 3 1 3 4 4 4 1 4 1 4 2 1 4 1 4 3 1 4 1 4 4 1 4 2 2 2 1 4 2 2 3 1 4 2 2 4 1 4 2 3 2 1 4 2 3 3 1 4 2 3 4 1 4 2 4 2 1 4 2 4 3 1 4 2 4 4 1 4 3 2 2 1 4 3 2 3 1 4 3 2 4 1 4 3 3 2 1 4 3 3 3 1 4 3 3 4 1 4 3 4 2 1 4 3 4 3 1 4 3 4 4 1 4 4 2 2 1 4 4 2 3 1 4 4 2 4 1 4 4 3 2 1 4 4 3 3 1 4 4 3 4 1 4 4 4 2 1 4 4 4 3 1 4 4 4 4 2 2 2 2 2 3 2 2 2 2 4 2 2 2 3 3 2 2 2 3 4 2 2 2 4 3 2 2 2 4 4 2 2 3 2 3 2 2 3 2 4 2 2 3 3 3 2 2 3 3 4 2 2 3 4 3 2 2 3 4 4 2 2 4 2 3 2 2 4 2 4 2 2 4 3 3 2 2 4 3 4 2 2 4 4 3 2 2 4 4 4 2 3 2 3 3 2 3 2 3 4 2 3 2 4 3 2 3 2 4 4 2 3 3 2 4 2 3 3 3 3 2 3 3 3 4 2 3 3 4 3 2 3 3 4 4 2 3 4 2 4 2 3 4 3 3 2 3 4 3 4 2 3 4 4 3 2 3 4 4 4 2 4 2 4 3 2 4 2 4 4 2 4 3 3 3 2 4 3 3 4 2 4 3 4 3 2 4 3 4 4 2 4 4 3 3 2 4 4 3 4 2 4 4 4 3 2 4 4 4 4 3 3 3 3 3 4 3 3 3 4 4 3 3 4 3 4 3 3 4 4 4 3 4 3 4 4 3 4 4 4 4 4

Good luck, but if you get caught, you didn't get it from me.

Plainglazed, It's not clear to me that there are 5⁵ codes. Those switches may be rocker switches in which case there may be 10⁵ codes! I tried to find out which it is on line, but I had no luck. Everything seemed to assume the reader knows what it is. Bummer. It's much harder to find a deBruijn sequence if there are 10⁵ codes, but I have a program to find one.

[plainglazed]

right on superp, see where you're coming from. agreed. what I found so amazing was the number of possible de Bruijn sequences. thought maybe if it was possible at all, there might even just be a unique solution. pretty cool.

[Guest]

Since the OP said 1-1-1-1-1-2 was 2 codes I'd say 1 and 2 are separate keys so 10⁵ codes.