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# Baldyville

## 79 posts in this topic

Flawed logic. The answer is infinity-1.

No one has EXACTLY 517 hairs. But you can have someone with 0, 1, 2,...516, 518.... eleventy billion... infinite

So given that your question allows for infinite hairs, there can be infinity-1 people.

Nooo! Look:

For a minute, let's pretend the "No person has exactly 518 hairs" condition DOESN'T EXIST.

If there were 519 people, no-one could have more than 518 hairs.

Each of the 519 people must have between 0 and 518 hairs.

No two people can have the same amount...

And there are only 519 possible values between (and including) 0 and 518

So this works....but every value has been used.

BUT...

We bring back the condition.

The value "518" cannot be used...

So if there were 519 people, let's count all the possible integers from 0 to 518 not including 518.

Oh. Now there are only 518 possible values.

518 values for 519 people...

And "518" is gone for good...

So there will be 519 values for 520 people -- doesn't work.

And 520 values for 521 people -- doesn't work.

And 1000000 values for 1000001 people -- doesn't work.

Therefore, you cannot go past 518.

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So an inhabitant can not have 518 hairs. It is no where specified that all inhabitants have to have any specific integer values. If there are 1000 inhabitants, then how many different values exist for hair count? 1001, because 0 is an option. Therefore, all 1000 inhabitants can have a different number of hairs AND include the rule of not have 518 hairs. For this, I say the answer is infinity since you have the extra number "0" to allow for hair count.

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Crap - I need to read the puzzle putting up a post sometimes. I retract my argument, because by rule #3, you lose that top endpoint value (so 1000 people, you not only lose the 518 value, but you lose the 1000 value, so you only have 999 possible values for 1000 people).

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Perhaps they could have rabbits tatooed on their heads, people will think they are hares (hairs).

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Ok, someone explain to me why there can't be infinity inhabitants? As 'there are more inhabitants than any inhabitant's hair in the town' = infinity, 'No inhabitant has exactly 518 hairs' = that's wonderful news(sarcasm), 'No two inhabitants have the same number of hairs on their head' = a useless fact as well.

It doesn't say there is a limit on 518 hairs, just that no one has exactly 518. Great?

Can anyone convince me otherwise?

So an inhabitant can not have 518 hairs. It is no where specified that all inhabitants have to have any specific integer values. If there are 1000 inhabitants, then how many different values exist for hair count? 1001, because 0 is an option. Therefore, all 1000 inhabitants can have a different number of hairs AND include the rule of not have 518 hairs. For this, I say the answer is infinity since you have the extra number "0" to allow for hair count.

Nice to see someone agrees.

I love how people start to insult others for not seeing their point of view, which is wrong so far as I can see.

Edited by Talent

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518

and one must be a bauldy otherwise no-one can live in the town

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The ANSWER is 518. you cant have 519 or more. We all can agree 0-517 are valid amounts of hair. There can't be 518 so your next amount would be 519 but that number and any number larger will not work Take number 519 for example. There is 0-517 and 519 which makes 519 people total and this is the same number of hairs on the head of 519. However rule three states there are more inhabitants than any inhabitants hair in town. Not the same or less therefore numbers 519 and up do not work.

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T = Total Inhabitants

H = Maximum Hair Count (T-1)

Th = total unique integers > -1 and <=H

By definition Th >= T (if you have less combinations than inhabitants, you are in violation - you can however have more based solely on this one rule for example 1 inhabitant has 3 hairs does not violate the uniqueness rule (although it does violate the 3rd rule)

So right now we have rule 1 covered (Th disallows duplicates) and Rule 3 ( Because H = T-1)

Rule 2 means that Th can not include 518 in the calculations.

To show mathematically this means:

If Th <= 518 it is calculated as H + 1 (0.1.2.3....H)

If th >518 it is calculated as H (0.1.2.3...516.517.519.520....H)

When Th = H we have violated one of the conditions of the problem.

Th >=T

H = T-1

Since Th = H (in our hypothetical) we can sub and get

T-1 >= T which we know to be false.

At th less than or equal to 518 we have

Th >=T

H = T-1

Th = H+1

H+1 >= T

(T-1)+1 >= T

T >= T which is true.....

Therefore 518 total combinations is 517 max hairs and 518 max inhabitants

I could have done it more accurately with H <= T-1 and do progession, but the problem called for Max, and therefore dictates H = T-1 (max possible inhabitants)

Edited by TySim

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Baldyville - Back to the Logic Puzzles

These are the conditions in Baldyville:

1. No two inhabitants have the same number of hairs on their head.

2. No inhabitant has exactly 518 hairs.

3. There are more inhabitants than any inhabitant's hair in the town.

What is the highest possible number of inhabitants?

Baldyville - solution

There can live maximum of 518 people in the town. By the way, it is clear that one inhabitant must by baldy, otherwise there wouldnâ€™t be a single man in the town.

Solution is simple. Let me try to explain this as well:

Always keep in mind that you are trrying to get the maximum nuber of inhabitants.

First condition is esy to understand. No 2 can be equal. Second condition is important, cant have exactly 518, keep in mind for the third condition. Third condition says to get the maximum number of inhabitants, knowing that the number of inhabitants is higher than the maximum number of hairs, on any one person in town.

True it does not say the numbers dont have to be consecutie, for example, inhabitant 1, 0 hairs. Inhabitants 2, 1 hair. and so on. People do it like this just to keep orginized in their brain.

Remember in order to meet the condition 3's requierments, there has to be a bald person.

You can say, inhabitant 1 has 20 hairs. But remember condition 3, you will now have at least 21 inhabitants in baldyville. So you would continue, inhabitant 2 has 15 hairs, inhabitant 3 has 9 hairs and so on, until you meet the requerment of condition 3.

Now, seeing that we can not use the number 518, saying there could be an infinit number if inhabitants would be incorrect. Say there is 1 inhabitant with 635 hairs on his head, you would now need at least 636 inhabitants to meet the requierments of condition 3. You are forced to use every number in the number line in order to get your answer. But seeing that we can not use 518 for the number of hairs on anyones head, any number greater 518 will give you a matching number, because of the fact we can not use 518 and we have to skip over it.

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The aside in the solution makes the given solution false. If one inhabitant is bald, then any number of non-repeating hair counts would equal the population of the city. If no one is bald, and there is no one with 518 hairs, then there could be an infinite number of people in the town, given that the person with the most hair has one less hair the the number of people in town

I disagree, consider having 517 people lined up with the number of hair on their heads in numerical order starting with one and going to 517. If you were to add one more person who is bald then you have 518 people with the largest amount of hair on one person 517. Thus you have one person bald, 518 people and the largest hair count is 517. For your second statement, if no one is bald and you have 517 people, and you add one more with 519 hairs (which is your only option) then you have 518 people and the largest hair count is 519. Your solution therefore, unfortunately, does not hold.

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only 517 be cause to go to 519 you have to have gone to 518 so only 517

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Surely it really is quite simple. If you consider that no one has three hairs on their head as it is easier to demonstrate, it should logically follow:

P = Person

H = Hairs

P H

1 0

2 1

3 2

4 4

5 5

As no person has three hairs on their head, person four must have at least four hairs as no one has the same amount of hair, and now the persons in the city and hair count are equal, and as was stipulated their are more people than hair, so it follows that three (or 518) is the maximum amount of people that can live in the city.

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Couldn't you just say the inhabitants were cats and dogs?

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person 1 - 0 (Must have more people than hair so to begin the 1st person in the city has to be bald so that the pop. is greater than the hair count)

Another way of stating the above is that if there were only one person in the city that person would have to be bald in order to keep rule number 3.

SOMEONE HAS TO BE BALD. Or else the number of hairs would be greater or equal to the number of people.

person 2 - 1

.

.

.

.

.

person 10 - 9

.

.

.

.

.

.

person 518 - 517

person 519 - 517 (Doesn't work - can't have two people with the same number of hairs)

person 519 - 518 (Doesn't work - no one has 518 hairs)

person 519 - 520 (Doesn't work - that would make more hairs than people)

There are more people than the greatest number of hairs. (Thus meaning at least one more)

No one can have 518 hairs

No Two people have the same number or hairs

And one person is bald.

Person # 519 would be the one with 518 hairs but no one does so the next number of hairs would be 519.

But then the person to hair ratio would be the same. However based on the rules you can't have an equal hair to person ratio... and you can't have more people than hair.

You have to keep the population greater than the hair count and the only way to do that is for person #1 to be bald and person #2 to have one hair and keep going until you get to person #518 who would have one less hair than his number which would be 517. Then #519 would have 518 or 519 which is not allowed because the number of people has to be greater than the number of hairs and you have to have a 518th person.

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Since someone can have 0 hairs, the person with the most hairs will always have one less hair than the number of people, for instance if there are 6 people, there are people with 0, 1, 2, 3, 4, 5, so the person with the most hair (the 6th person) will have 5 hairs. As soon as a number is omitted, that bumps up the max number of hair to be equal to the number of people for all greater values of people, which violates the 3rd condition.

So if there are 518 people, the person with the most hair will have 517 hairs. If a 519th person is added, they would normally have 518 hairs, which violates condition 2, so they must have 519 hairs, which violates condition 3. If a 520th person is added, they would have 520 hairs and so on.

So the max number of people is 518.

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Is it possible for there to be more than 1 bald person - since they don't have any hairs to count so the number of hairs is irrelevant. (It is baldyville and they probably wouldn't have named it such unless there were more than one bald person?)

Only the people with hair can be included in the pattern of one hair more than the last

Six bald people and you could have 524 people?

eighty bald people and you could have 588 people?....and so on?

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Baldyville - Back to the Logic Puzzles

These are the conditions in Baldyville:

1. No two inhabitants have the same number of hairs on their head.

2. No inhabitant has exactly 518 hairs.

3. There are more inhabitants than any inhabitant's hair in the town.

What is the highest possible number of inhabitants?

Baldyville - solution

There can live maximum of 518 people in the town. By the way, it is clear that one inhabitant must by baldy, otherwise there wouldnâ€™t be a single man in the town.

No inhabitant has exactly 518 doesn't mean an inhabitant couldn't have 555, or 1000 or a 1,000,000.... so I still don't get this and it is going to trouble me for the rest of the day!

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No inhabitant has exactly 518 doesn't mean an inhabitant couldn't have 555, or 1000 or a 1,000,000.... so I still don't get this and it is going to trouble me for the rest of the day!

Forgive my limited experience in this matter, but...

Would I be right to say, that someone with 555 hairs still has 518 somewhere on his head?

Rule 2 I think, states that no one can have 518 hairs on their head exactly.

Would I be right to say that this is not saying 518 hairs total?

I'm moments away from understanding this, and if the answer to the above questions are yes, I'm golden.

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Ok took me some time to understand but now I get it I think.

You always need at least 1 person more than the max number of hairs on the most hairy of your villagers.

If you have a person with 319 hairs, you have at least 320 villagers. All villagers have a different amount of hairs on their head. That means to get to 320 villagers you have to count EVERY single one including the bald one as noone can have the same amount of hair.

If you exclude that someone has 518 hairs you lose one villager to count. Remember you need to count all the villagers to get 1 more villager than the most number of hairs on a head. If you lose 1 villager through the exclusion of 518 hairs, you will always end up 1 villager short to meet the condition to have at least 1 more villager than max hairs on the head.

Increasing the numer doesnt change that. If you assume you have a villager with 1000 hairs, you would need 1001 villagers. As all have different numbers of hair on their head you need to count ALL starting from 0,1,2,3,4 ...... 999,1000,1001. But as you lost the number 518, you can never reach the number of 1001 villagers but only 1000. Thus you violate the conditions, meaning you can not have more than 518 villagers (counting the bald one).

Did I get this right now? <_<

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There is no correct answer. You didn't say the maximum amount of hair on somebody's head. One person could have over 1,000,000 hairs .

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Baldyville - Back to the Logic Puzzles

These are the conditions in Baldyville:

1. No two inhabitants have the same number of hairs on their head.

2. No inhabitant has exactly 518 hairs.

3. There are more inhabitants than any inhabitant's hair in the town.

What is the highest possible number of inhabitants?

The answer to this problem is false. There is no concrete solution as there can be an infinite number of people according to the conditions presented.

It is NOT 518 because the rules state that no two people can have the same number of hairs and also that there simply must be more inhabitants that the inhabitant with the highest hairs. It says nothing about ordering. Somebody could have 517 hairs and the next 519 without having to realistically(not that this problem is) have 518 hairs at some point. It could also have 1 million people to 517 hairs. It just says MORE not one more or two more etc. Just MORE. As long as there are more inhabitants than the highest inhabitants hair, the equations is satisfies given that the number of hairs never equals zero.

Jenna

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The answer to this problem is false.

Somebody could have 517 hairs and the next 519 without having to realistically(not that this problem is) have 518 hairs at some point.

No one can have 519 hairs.

It could also have 1 million people to 517 hairs.

How many hairs does the one millionth person have?

Let's use the same conditions but change "No inhabitant has exactly 518 hairs" to "No inhabitant has exactly 2 hairs."

We can have one person with no hair. That works.

We can have two people. One with no hair and the other with one hair.

Can we have three people? Tell me how many hairs each of these three people have on their heads.

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No inhabitants have 518 hairs.. its a trick question.. there is an unlimited number of people.. someone can have 517 or 519 hairs

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This is the most retarded question i ever tried to answer! There is no answer, it can be any number, just because you said no one has exaclty one number of hairs on their doesn't mean they can't have more than that amount. So if you say no one can exactly 50 hairs on their head it doesn't mean they can't have 51 or 52 and so on. Maybe i am just not getting it i don't know but if someone can answer this better than he did please feel free to explain!

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I have exactly the same issue with this puzzle as sdy4444. Why cant someone have 1000 hairs? Nowhere does it say that you cant have MORE then 518. It says you cant have that exact number ... Am I being dense or does this puzzle need some work?

im with you why not a million hairs? or more?

no way to know 4 sure