math riddles...

[VJ]

Hello,

I'm struggling with these math riddles (the solution for the first just seems so easy)

1. A fictional city
- no two inhabitants have the same number of hairs
- no one has 302306 hairs
- there is nobody with equal or more hairs than inhabitants
- there are no 1000 people that have a birthday on the same day
How many inhabitants can there be at most ?

And for another riddle, I really have no clue (yet ?):
2. Complete the sequence
31 41 59 26 ??


Any suggestions ?


Jörg

[Dogbert]

Ok, for the 1st riddle:

Since there aren't 1000 people with the same birthday, 999*365 = 364,635 (max number of inhabitants)
There is no inhabitant with 302306 hairs
No inhabitant has a number of hairs > or = to the number of inhabitants.
This means 364,635 - 1 (for the number 302,306) -1 (number 364,635 since nobody can have this amount of hair) + 1 (we have bald one !!!) = 364,634

At least that's my guess

[dZeus]

1. 302306 ?

Suppose every inhabitant is numbered by the amount of hairs he has. Start with inhabitant #1, and think of inhabitant # 302306 being the bald one. You can't have any more, because then you would end up with an inhabitant with the same number of hairs as there are inhabitants

2. no clue

[VJ]

Originally posted by Dogbert
Since there aren't 1000 people with the same birthday, 999*365 = 364,635 (max number of inhabitants)
There is no inhabitant with 302306 hairs
No inhabitant has a number of hairs > or = to the number of inhabitants.
This means 364,635 - 1 (for the number 302,306) -1 (number 364,635 since nobody can have this amount of hair) + 1 (we have bald one !!!) = 364,634

Yes, that is what I thought (but I used 999*366, as the question concerns a worst case scenario and a leap year has 366 days ).
An additional question: does someone with 302307 hairs have 302306 hairs ? Dobert apparently chose "no", where dZeus chose "yes"... I would be tempted to choose no, again for having the worst case as high as possible.

But the solution (in either case) is so simple, that I don't really trust it. (knowing where I got the question, they usually are much more difficult).

Jörg

[Ribbit]

The second one appears to be the digits of pi.

[Dogbert]

Originally posted by Ribbit
The second one appears to be the digits of pi.

Yes

3.1 41 59 26 53 6. . .

[GNEP]

So searching for a pattern is not going to get you anywhere...

3.1415926536 is all I can remember offhand (edit: except I think that the last digit is a rounding, so should be a "5"...).

what about:

271 828 182 845 ?

[VJ]

Originally posted by Ribbit
The second one appears to be the digits of pi.

Great find ! In another question (concerning a circle and a rectangle) they mention that "as a reminder, pi=3.1415926535897....", but you don't need pi for that question. Guess this is their hint for the last question.

GNEP: hehe....

Jörg

[dZeus]

Originally posted by VJ
Yes, that is what I thought (but I used 999*366, as the question concerns a worst case scenario and a leap year has 366 days ).
An additional question: does someone with 302307 hairs have 302306 hairs ? Dobert apparently chose "no", where dZeus chose "yes"... I would be tempted to choose no, again for having the worst case as high as possible.

But the solution (in either case) is so simple, that I don't really trust it. (knowing where I got the question, they usually are much more difficult).

Jörg

I fail to grasp what you mean there... I didn't say that there can't be more than 302306 people because people with 302307 hairs also have 302306 hairs...
It would be quite safe to assume that they only prohibit people with the exact amount of 302306 hairs.
However, you can't have any more, because with every amount of inhabitants larger, you would end up with the 'last' inhabitant having at least the same amount of hairs as there are inhabitants.

(I hope this makes sense)

[VJ]

hmm, yes, it does make sense...
I see your point


Jörg

[dshumake]

Originally posted by GNEP
So searching for a pattern is not going to get you anywhere...

3.1415926536 is all I can remember offhand (edit: except I think that the last digit is a rounding, so should be a "5"...).

what about:

271 828 182 845 ?

e

[GNEP]

e-yup!

[thop]

http://members.shaw.ca/vseward/pi_main.html

[gt40]

for a minute I was rather intrigued with the notion of memorizing pi (must be my math/physics background), then I remembered - I HAVE A LIFE!

[Umfriend]

I have another one, but I need to cover one basic thing first:

1 divided by 3 is 0.33333 and endless 3s. What is the notation u use for infinitly repeating figures?

We use 0.3 with a forward slash through the 3 (but I can;t get that in this post). Can we agree 0.3/ means 1/3?

If so, prove 0.9/ equals one....
Umf