# icepick1346

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## icepick1346's Activity

1. icepick1346 added a post in a topic

They cannot pull the lever multiple times...

The answer is the Hamming Code as pointed out by Adiace....
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2. icepick1346 added a post in a topic

3. icepick1346 added a post in a topic

I agree with this answer...
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4. icepick1346 added a post in a topic

The basic idea of the Hamming Code (first given by Adiace) is that there are 26 "data signals" (for each jar) and 5 "check signals"... IF the warden intercepts a "data signal", then at least two "check signals" will be wrong and will specifically identify which of the "data signals" was compromised... On the other hand, IF the warden intercepts a "check signal", it will be the only one wrong; if there's only one wrong "check signal", that tells you there are no problems with the "data signals"...

If you are numbering the signals 1-31, the "check signals" would be signals 1,2,4,8 and 16... the first jar would be represented by jar 3 and all subsequent non-"check signals"...

Each "check signal" adds up the number of balls in all jars where (signal# mod(checksignal#))=0 and signal#>checksignal#... For an even number of balls that check signal would send one signal (say green), and for even number it would send the other signal (say red)...

Once all the signals are received, the lone prisoner will check that all the check signals are either true or false... Like I said above, if only one check signal is false, the all the data signals are OK... If more than one check is false, you simply add the position of those signals together to identify the signal that was compromised; for example, if check signals 1, 2 and 8 were false, you would know that signal 11 was compromised and would reverse the signal (in this case referring to jar #7...

That's the basics of the Hamming Code...
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5. icepick1346 added a post in a topic

I agree, but I won't be able to work the math till I get home later...
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7. icepick1346 added a post in a topic

I believe Adiace is correct, with the exception that the five "check" prisoners be interspersed with the others... And it can't be a coincidence you get 31 prisoners since you need that many for this solution...
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8. icepick1346 added a post in a topic

The problem is not just figuring out how many balls there are but which jars the balls are in... I like your idea, but it doesn't let the lone prisoner replicate the exact pattern of the original jars...
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9. icepick1346 added a post in a topic

NEVERMIND, there's not enough info to isolate the problem anymore...
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10. icepick1346 added a post in a topic

Doh!!!

Guess I didn't think about that... let's see...

That should take care of the previous problem I had... And again, the first and last ball will provide the ability to identify if (and where) the intercept occurred...
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11. icepick1346 added a post in a topic

i haven't thought it all the way through, but i think it's SIMPLE and WORKS...

I don't think there's any way to mess this up...

EDIT: The intercepted error may not show up right away, but the first and last balls will verify all the information in between and identify any faltered communication... The intercepted communication will have ACCURATE information on either side of it that will help reconcile the false info...
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