78 replies to this topic

[logic seeker]

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

[Woodrow Davis]

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.

[Mazdo]

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

[myers0810]

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.

[Mr Widdle]

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.

[jules2]

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?

Just asking!

[Sandinator]

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?

Spoiler for Solution

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 wouldn’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!

[paulbob]

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.

[Konstantin]

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? <_<

[Bomb]

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 .