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Topic: Stair MASTER (Read 711 times) |
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Noke Lieu
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Stair MASTER
« on: May 10th, 2004, 10:39pm » |
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Poor willy wutang.
Snuffed it at last.
And for being the subject of feindish puzzles, is sentenced to eternity climbing stairs. Harsh afterlife too, it seems.
But, work place relations being what they are, its only fair that a demon is destined to count out each and every step Willy makes. In English English.
To make it a bit more interesting, and pass the time, Willy and the demon make a race of it- can I climb faster than you can count?
Whomever completes their task first has to wait until the other has finished theirs too. But no rest time for the loser.
Sadly, climbing stairs is still an effort, even when you are ethereal. Thus after each step, Willy slows a little. Unless he can catch his breath a little by winning a step of the race.
Going to leave estimates up to you. Half of this is coming up with them.
At what steps (roughly) will Willy's fortunes reverse in this race?
(inspired by last night's washing up)
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| « Last Edit: May 10th, 2004, 11:58pm by Noke Lieu » |
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a shade of wit and the art of farce.
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Cathos
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Re: Stair MASTER
« Reply #1 on: May 10th, 2004, 10:57pm » |
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It seems that if Willy can keep a good pace after a few thousand steps, he should be able to win the race. I imagine it takes longer to say "fourty seven thousand, eight hundred and ninety two" than it does to climb one step. Of course, by this point, poor Willy is probably crawling up the steps.
If he can manage to recouperate in the two seconds he'll gain at this point, I imagine he'll do fine. This is all assuming that a demon can only count as fast as I can - perhaps a poor assumption to make...
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Sum Arbor
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Noke Lieu
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Re: Stair MASTER
« Reply #2 on: May 11th, 2004, 12:02am » |
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Lets keep the demon talking at medium rate. Not West-Country (pirate like), not Geordie (way WAY too fast)  .
By my reckoning, willy is going to have a rough time every 1000 for a while. Really nasty every million etc...
Don't reckon two seconds is much recovery time. Definately not back to an initial level. Try taking the stairs to work next time. As fast as possible.
That's only first couple of hundred... pretty pooped after that.
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| « Last Edit: May 11th, 2004, 12:05am by Noke Lieu » |
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Icarus
wu::riddles Moderator
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Re: Stair MASTER
« Reply #3 on: May 11th, 2004, 3:34pm » |
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Having agreed to the race, willy should take his own sweet time. At first, he will fall way behind, but the demon's job grows (if only logarithmically), while his does not. After a year willy will be able to go at a very slow rate. After a few years, willy will be able to spend days doing something interesting between each step, while the poor demon rolls out digits. Somewhere along the line, the demon is going to realize he is the one being tortured, not willy!
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"Pi goes on and on and on ...
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I wonder: Which is larger
When their digits are reversed? " - Anonymous
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Cathos
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Re: Stair MASTER
« Reply #4 on: May 11th, 2004, 7:54pm » |
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I was under the impression that the Demon had wait until Willy reached the step - So he says "ten" then waits till Willy get from 9 to 10, then says "eleven", waits till he goes from 10 to 11, etc.
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Sum Arbor
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Noke Lieu
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Re: Stair MASTER
« Reply #5 on: May 11th, 2004, 11:30pm » |
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Yeah, Willy a clever fella. That's why he escaped islands, had fantastic sexual exploits etc etc etc.
But WHEN is willy on a roll, roughly. It doesn't take much time to say "septillion and one" etc.
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a shade of wit and the art of farce.
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towr
wu::riddles Moderator
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Re: Stair MASTER
« Reply #6 on: May 12th, 2004, 12:32am » |
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Willy should just trick the demon into counting in unary 
one
eleven
a hundred and eleven
one thousand one hundred and eleven
eleven thousand one hundred and eleven
etc
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Wikipedia, Google, Mathworld, Integer sequence DB
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rmsgrey
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Re: Stair MASTER
« Reply #7 on: May 12th, 2004, 3:02am » |
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on May 11th, 2004, 11:30pm, Noke Lieu wrote:| It doesn't take much time to say "septillion and one" etc. |
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But the amount of time saying "septillion and one" compared to the amount of time spent saying "septillion, five hundred and thirty seven sextillion, four hundred and twenty six pentillion, eight hundred and forty two quadrillion, four hundred and ninety five trillion, eight hundred and thirty one billion, two hundred and fifty seven million, eight hundred and forty nine thousand three hundred and eighteen" is very small even when you just consider the individual numbers. When you consider the proportion of steps where you have better than 80% (say) of digits non-zero, picking 103n as your example seems a little churlish. Besides, while 1024 ("septillion"), or even 10303 ("centillion") may be easy to say, there are plenty or numbers which aren't going to be so easy (1010,000,000,000 (10^(10^10)) say).
Of course, this is largely a red herring since the question isn't when can Willy stop bothering to hurry and still keep ahead of the demon indefinitely, but when does Willy get the advantage, and that's going to be much sooner - spending the odd hundred or thousand steps with no rest is going to stop getting any harder fairly quickly - I'd guess by the billion mark things will be firmly in Willy's favour. Of course, the flip side is what Willy is supposed to do while waiting for the demon to finish reciting syllables? When he's restricted to less than one step per hour, or even day, and has to spend the rest of the time listening to the demon spouting gibberish (lets face it, any number that takes an hour to recite might as well be gibberish - unless you can express it concisely enough to be handled by a human mind) I imagine Willy could get quite excited about Graham's number, anticipating a period of swift progress ("Graham's number minus a centillion", etc being far and away the most concise way of expressing numbers in that region)
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Three Hands
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Re: Stair MASTER
« Reply #8 on: May 12th, 2004, 4:45am » |
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Well, I reckon Willy should just take as long as he likes per step, given that early on it will just make sure that the demon is kept waiting, and he conserves his energy until he gets some easy rest stops after a couple of hundred or so. Failing that, it means it will be the demon getting bored waiting for Willy to finish taking a step, and so might cause some interesting conversations, possibly even the popular riddles in hell at that time 
Of course, once the demon is condemned to spouting gibberish for days on end, Willy can take his time studying to be a chess grandmaster, and so be prepared to take on the Grim Reaper, return to life, and enjoy life once more, assuming he's allowed to do that after such a long period in hell...
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hi
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could he walk/roll/fall down the stairs. therefore the demon also has to add negative/minus
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