1. no justin wrong

if its zero why did it take them 7 days to figure out???

2. ## Hmm...

How can they console their superb reason with faith?

biterman.

PS: I'd love to know the answer to this. Something tells me it's exceedingly simple, and when we find out we're just gonna smack ourselves upside the head for not realizing it.

3. Okay, first the story edited to get the bare facts

in a group are some who have a mark.
the mark is only visible to others.
no one gets to know if s/he wears a mark
7 times they met until finally, all marked left.

You didn't tell how many people were in the group.
That leads to the conclusion that this fact is not important.

You did say you wanted proof, so the seventh gathering
was NOT a random success.

No group can determine such facts with EXACTLY seven
tries if the size is variable. A group of two will have the
perfect solution after 4 tries AT LEAST. And with any luck
way before that. And that would be a random success.

So that leaves us with either possibility: None or All.
Neither would take 7 days to figure out, but again a random
time, depending on how they check.

There is no way to make sure that while testing you do not
accidently hit the right number by leaving the marked out of
the test. So there is no way to make sure it takes EXACTLY
seven tries. No matter how large the group is.

Which leaves me with the conclusion that the bare mathematical
facts are not important to solve this riddle, or rather it can't be
solved, which would be another kind of solution.

So lets get back to the seemingly unimportant facts.

The priest started sunday. They figured out the next sunday.
Depending on the religion, could it be all their sins are forgiven
before sunday service ?

Then, without telling they could have found another way...
maybe the just silently jailed all the sinners or something.

?

4. I'm stumped!!

5. nvoigt said
>>>>>No group can determine such facts with EXACTLY seven
tries if the size is variable. A group of two will have the
perfect solution after 4 tries AT LEAST. And with any luck
way before that. And that would be a random success.

no they can even if the group is variable in size
remember they are superintelligent beings(something like an islandful of mensa members(i wouldn't lke to live in such a place though)

another hint i'll drop
>>>>
try figuring out the 7 days part of it
and as i said before try mathematical induction

that means something like

if P(1) is true and p(k) implies p(k+1) then p(n)(generalisation) is true

and no the answer is not very obvious
to us non superintelligent beings

i was stumped for a week with this first time i heard this and am yet to see a person who answered this correctly without hints and prodding

so lets see if thisboard can produce someone

when you peepl get bored tell me i'll post the answer

6. Well,

1 Person will have a solution in 2 tries
2 persons will have a solution in 4 tries
3 persons will have a solution in 8 tries

AT LEAST !

Fact is, they try until the priest says it's ok.
No try will reveal anthing about anybody,
as the priest will not say why this is the
wrong combination ( could be a sinner in,
could be a sheep missing ).
So they can as well hit the right combination
on the very first try. We don't know which
with all out, or all in. It's completely beyond
our control or knowledge, so it's nothing we
can build our proof on.

With this kind of feedback from the priest
( Yes/No ) and two different error conditions
( sheep missing / sinner in ) you are lost.

I'm eager to get an explanation, though ;-)

7. nvo

no you are missing something here
1 person needs 2 tries is wrong

why dont you peepl try and use the data provided
no one to my knowledge has used the data abt 7 days yet

another hint
the solution requires no form of communication at all
all the people need to do is to come to church
and watch

jv

8. I'm not taking in account the priest here... it's just one more
person. If neither person where a sinner, there wouldn't be a
task, so there has to be at least one.

1 Person...

assume he's a sinner:

Goes -> Error
leaves -> Right
2 tries

leaves - > Right
1 try

assume he's a sheep:

Goes -> Right
1 try

leaves -> Error
goes -> Right
2 tries

4 possibilities, all same probability, 6 tries, statistically that makes
1.5 tries. Actually, it depends on luck, and implying you need
logic and not luck, you need 1 to be sure, and another one to
make the right decision to leave or stay. Assuming that happened
on the first try is not something you can build a proof on.
Assuming a statistical middle way is also nothing you can build
a proof on. So either it's all luck, or you assume 2 tries...
As we all know from binary calcs, this is like a bit...
1 bit, 2 states, 2 bits, 4 states, 3 bits, 8 states... and you will
have to test them all to know which is right, and hitting the
right combination anytime is pure luck. You don't need all tries
most of the time.

Actually, you need one try less, because the group can assume
that all sheep is not an option.

1 -> 1
2 -> 3
3 -> 7

ah, the magical seven... which doesn't mean we know how many
it were... that completely depends on how they test. They could
hit the right combination on the very first day...

I'm going to try your way...

X people needed 7 days to identify Y sinner(s)
X people needed 7 days to identify ( X - Y ) sheep
( whatever is shorter )

Obviously, X is at least 3, or it gets really ridiculous.
Y should be at least 1 or the task is fullfilled the
second it was spoken out.

I'm stumped here...

>no they can even if the group is variable in size

Do you realize what you want to prove here ?
You want to prove that with seven instructions you can
compare any two binary streams for equality, regardless
of size. You should break that knowledge to some
database corporations. I bet Oracle or Microsoft would
kill a small country to obtain that strategy and patent it.

9. Originally posted by nvoigt

>no they can even if the group is variable in size

Do you realize what you want to prove here ?
You want to prove that with seven instructions you can
compare any two binary streams for equality, regardless
of size. You should break that knowledge to some
database corporations. I bet Oracle or Microsoft would
kill a small country to obtain that strategy and patent it.
i dont think you are quite on the rite track here

they dont go by the trial and error method they think it out and keep their eyes open that is all

10. Sorry, without communication and an infinite amount of people, I see no chance of thinking it out...

Can you give the solution ?

11. to nvo

no i wont give out the soln in public
let otherpeoplethink abt it
i can do so in private if you want though

ill give you a step towards the answer now
priv ok

12. ok, let the others have fun...

I for one surrender. Can you send a solution to

Niels.Voigt@T-OnlineXXX.de ?

oh, and delete the XXX after T-Online, i hate webspiders

13. ok nvoigt

i've pmed it to you and mailed it too

tell me if you get it?

jv

14. There were two essential facts missing. First, that they apparently meet every day. I thought the seven days was just implying "next Sunday when they met again". So they meet once a day?

In that case (2.) how do they discover they have the mark? Is the priest allowed to say something? Your description made it seem that there would be no way for anyone to discover if they have it or not. But if the priest can say (three today) or even (one gone today, three sheep missing) then that changes things quite a bit.... or did I just miss this piece of the puzzle? Presumably, they meet once a day for seven days, hence they must discover they do or don't have the mark by meeting once a day for seven days... right? Wrong? If this is too much of a give away, please PM me... ;p

15. Well...

In reality I would think that everyone that had the mark would be stared at considerably by everyone else.

So if you deduce the number of people it would take to stare a number of people out over a seven day process, I would think that you would have the answer.

I am going to think along these lines. Am I off....?