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        riddles >> medium >> Wheel Combos - Answer Machine with Wheel Locks
        
(Message started by: TenaliRaman on Jan 3^rd, 2005, 7:02am)

Title: Wheel Combos - Answer Machine with Wheel Locks
Post by TenaliRaman on Jan 3^rd, 2005, 7:02am

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?

Title: Re: Wheel Combos - Answer Machine with Wheel Locks
Post by Grimbal on Jan 3^rd, 2005, 7:10am

If I understand the problem correctly, it is ::[hide]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.[/hide]::

Title: Re: Wheel Combos - Answer Machine with Wheel Locks
Post by THUDandBLUNDER on Jan 3^rd, 2005, 10:55am

Quote:

This time...

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.

Title: Re: Wheel Combos - Answer Machine with Wheel Locks
Post by JocK on Jan 3^rd, 2005, 12:27pm

on 01/03/05 at 10:55:03, THUDandBLUNDER wrote:

.. either Grimbal's interpretation of a poorly-worded puzzle is wrong or it is trivially easy.
I supect the former.

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?

Title: Re: Wheel Combos - Answer Machine with Wheel Locks
Post by TenaliRaman on Jan 6^th, 2005, 11:10pm

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