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Baldyville


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#21 KBHoleN1

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Posted 28 August 2007 - 04:47 PM

Baldyville
These are the conditions in Baldyville:
1. No two inhabitants have the same number of hairs on their head.
2. No inhabitant has exactly 3 hairs.
3. There are more inhabitants than any inhabitant's hair in the town.
What is the highest possible number of inhabitants?


Let's substitute 3 for 518 so it's easier for you people to count. Note the bold line - stop being so damn picky and take it at face value (the intent of the puzzle) - it means that the number of people in town (p) is greater than the number of hairs on any one person's head (h) (p>h).

So person 1 is bald (p=1, h=0).
Person 2 has one hair (p=2, h=1).
Person 3 has 2 hairs (p=3, h=2).
No one can have 3 hairs, no one ELSE can have 0, 1, or 2 hairs on their head, because they're already taken.

So you have 3 people, no one has more than 2 hairs (meeting condition 3). If person 4 were to have 4 hairs, you would have p=4 AND h=4, which cannot happen (condition 3, 4 is not greater than 4). The same applies to any person after this (5, 6, 7, ...). Once you skip a number, assuming you can't repeat, condition 3 prevents the existence of more people, because the number of hairs will be equal to the number of people.

Therefore if the number skipped is 518 (instead of 3), the maximum number of people is 518.

If you still don't get it, I feel sorry for you.
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#22 jkeen5891

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Posted 01 September 2007 - 06:49 AM

Ok it took me a while to get this but maybe I can explain it a little better, with a different style of thinking.
At first I thought there could be an infinite number. Lets say 1000 for example. The reason there cant be 1000 is there has to be more people than hairs on one head. So if there are 1000 habitants then you have to start counting... Habitant 1 (0 hairs) Habitant 2 (1 hair) Habitant 3 (2 hairs). You will do this all the way up to 518 Habitant (517 hairs) Then try to go forward 519 Habitants (518 hairs, can't do that).
And it has to go in order like there, the rule doesnt say it has to be consecutive but thats the only way it works. If you have 518 Habitants there has to be 518 different hair combinations and none of them can be 518 or higher.
This all "clicked" when I tried to do a number over 518. I thought "well it doesnt say it has to be in order so there can be a bald guy and a guy with 4 hairs and a guy with 1000. But thats where the rule 3 comes in. In order to get a million inhabitants you have to have 1000 combinations, and you cant count to 1000 if you cant go over 518. If you try to skip 518 or any other number before it as some people suggested, when you get to the end you will end up with the 1000th person having 1000 hairs. 3. There are more inhabitants than any inhabitant's hair in the town.

Does this help? Its kind of like explaining a color to a blind person. You either get it or you don't but once you see it, you know what it is.
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#23 SPENGLER

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Posted 09 September 2007 - 08:56 PM

there is nothing stopping you from skipping a hair count: 0, 1, 3, 4, 20

except if you skip a hair count, then you need to have that many people in town (+ 1). so the above example works well, and shows that their must be 21 people in town. okay easy. back fill the missing hairs ... 0,1,2,3,4,...,20 == 21 people.

this works just fine until you reach the X+1 person. let's say we have 5 people: 0,1,2,3,519. when we attempt to backfill to catchup and have 520 residence, we skip 518, and can no long give the 520th person hair as the only number left is 518; without breaching the 519 mark and having to re-backfill again. 0,1,2,3,...516,517,519 and one extra dude.

if we simply pop off one hair on the last dude, then we can easily start backfilling.
1) 518 people, where no one person has 518 or more hairs.
2) we've already proven that 519 (or any number higher is unpossible)
3) and "skipping" numbers while backfilling would be disadvantageous as you may as well maximize on your population .... and thus satisfy the "what's the maximum population" bit.
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#24 memphobaribabe

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Posted 19 September 2007 - 03:51 PM

You guys have missed the most obvious part of the riddle..... the title.
Baldyville
this title implies that there can be an infinite number of people in the town as long as they were all bald. If they are bald they have no hair to be judged by. They can not have the same amount of hair on their head if they have no hair to begin with. The riddle also says that no two people can have the same amount of hair as any other inhabitant ON THEIR HEAD. So, get rid of the hair and everyone in BALDYville is happy.

Just trying to change it up.
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#25 bonanova

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Posted 19 September 2007 - 09:35 PM

If they are bald they have no hair to be judged by. They can not have the same amount of hair on their head

Interesting.

0 does not equal 0.

But let's keep this a secret, OK?
Word gets out, imagine the recall of all those text books.

Would be devastating.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#26 ftucker56

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Posted 16 October 2007 - 07:59 PM

The criteria for determining any number at all is actually not met. It stipulates that no inhabitant has EXACTLY 518 hairs, it doesn't stipulate that no inhabitant had more or less than 518 hairs. Is it me or are there a lot of people making something out of this that just isn't there? Spell check could stand to be used on this also.
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#27 credels

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Posted 16 October 2007 - 10:53 PM

Does this include moustaches, beards, ear & nose hairs?
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#28 Gavin2k7

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Posted 30 October 2007 - 05:19 PM

Where does this imply that the # of hairs has be be in increments of 1.

There might not be anyone with 1 - 50 hairs on their head.
Therefore unless it is stipulated that the # of hairs is incremented by 1 from person to person, then there could be any number of people.
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#29 aishi_khurana

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Posted 09 November 2007 - 09:04 AM

saying dat nbdy has xctly 518 hair on their head dsnt mean people cannot ve 519 ,517 or for cat matter 520
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#30 ftucker56

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Posted 09 November 2007 - 04:34 PM

To Credels:
The teaser states "on their head"
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