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Topic: Wheel Combos - Answer Machine with Wheel Locks (Read 773 times) |
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TenaliRaman
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Wheel Combos - Answer Machine with Wheel Locks
« on: Jan 3rd, 2005, 7:02am » |
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This time willy replaced the old keypad-based answering machine with a very old one where u have dial wheels with numbers instead of a digital pad. So this answering machine consists of 4 wheels, each numbered sequentially 0 to 9 (with 9 next to both 8 and 0.) How many wheel turns (changing one digit by one value) are needed to attempt every combination and possibly break the code?
-- AI
Hmm i hope this is not discussed in answer machine hacking?
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| « Last Edit: Jan 3rd, 2005, 7:04am by TenaliRaman » |
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Grimbal
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Re: Wheel Combos - Answer Machine with Wheel Locks
« Reply #1 on: Jan 3rd, 2005, 7:10am » |
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If I understand the problem correctly, it is ::9999, i.e. you can go through all numbers by changing one digit at a time, by one unit. This assumes you choose your starting number and your first try counts as 0 turns.::
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ThudnBlunder
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Re: Wheel Combos - Answer Machine with Wheel Locks
« Reply #2 on: Jan 3rd, 2005, 10:55am » |
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Quote:This is not a stand-alone puzzle. As such, it is therefore unintelligible to all but you cognoscenti. 
Anyway, either Grimbal's interpretation of a poorly-worded puzzle is wrong or it is trivially easy.
I supect the former.
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| « Last Edit: Jan 3rd, 2005, 11:03am by ThudnBlunder » |
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THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
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JocK
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Re: Wheel Combos - Answer Machine with Wheel Locks
« Reply #3 on: Jan 3rd, 2005, 12:27pm » |
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on Jan 3rd, 2005, 10:55am, THUDandBLUNDER wrote:
.. either Grimbal's interpretation of a poorly-worded puzzle is wrong or it is trivially easy.
I supect the former. |
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I think some constraint applies to the dialing: e.g. the dialing wheels can only make right turns, one click at a time. But even then Grimbals answer is correct: considering two dialing wheels one simply goes through the sequence:
00 > 01 > .. > 08 > 09 > 19 > 10 > 11 > 12 > .. > 17 > 18 > 28 > 29 > 20 > 21 > .. etc.
One never needs to make more than one click to obtain a new number. The same applies to the third and fourth dialing wheels.
What further constraints do you have in mind TenaliRaman?
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| « Last Edit: Jan 3rd, 2005, 12:29pm by JocK » |
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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TenaliRaman
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Re: Wheel Combos - Answer Machine with Wheel Locks
« Reply #4 on: Jan 6th, 2005, 11:10pm » |
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Sorry for the delay and excuse me for the poor wording of the puzzle.(Giving exams 3 times a week during **holidays** isnt doing me any good obviously).
The extension that i had in mind.
Given a directed graph of 10000 nodes such that each node has 8 incoming link and 8 outgoing link, show that this graph has a hamilton path.
I think this is right!
And if it is, then i wonder whether T&B would have appreciated this one to be in medium (if i had given the extension before the original wheel combination question) or is it again trivially easy.
-- AI
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| « Last Edit: Jan 6th, 2005, 11:12pm by TenaliRaman » |
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