Hi, I have to admit I am new to this forum, but it looks very good! I'm a 14 year old maths freak, so I often look up previous past maths competitions, papers etc, and analyze them. However I am stuck on this particular question. I was wondering if someone could give me guidelines on ways to solve it, and what sort of catergory this sort of problem falls under? It is quite unique.



Yenko the Bulgarian goatherd drives his father’s goats into a valley each morning and lets them browse there all day before driving them home in the evening.

He notices that each morning the goats immediately separate into groups and begin to feed. The number and sizes of the initial groups vary. Some days there are nine or more groups; on other days, there are three or fewer. There can be groups of one or the whole herd can form a single group.

About every five minutes one goat breaks away from each feeding group and these breakaway goats form into a new group.

Yenko has noticed that by the afternoon, even though the goats continue their regrouping, the sizes of the groups have stabilized, and there are always seven feeding groups.

a.) How many goats are there in the herd?
What are the sizes of the feeding groups once they have stabilized?

Yenko’s father then sells two of the goats. Over the next week, Yenko notices that things have changed. The sizes of the feeding groups no longer stabilize. There are not always seven groups. Nevertheless, a cyclic pattern of sizes develops every day.

b.) Find at least two possible cyclic patterns of sizes.

javalex

I cannot see where to start on this. There does not seem to be enough information. I think you should give a partial solution. Yassou!

ektanetgurl

That's a problem from the maths challenge. your not allowed to ask people on the internet. the first one's EASY ;D but i'm still working on the 2nd one.

javalex

Yo! So where am I allowed to discuss this?
It seems a little un-inviting to be told I am not allowed to do something that I would like to do.
Yassou!

ektanetgurl

soory i meant u can't talk 'bout it if you've entered the challenge!!
I have a really weird brain that thinks the whole world knows wat i'm thinking!! :
I found the ans 2 the 2nd dough!
it's just using your common sense!
think on it. . .

javalex

Yo! Well, my situation remains; I cannot see where to start on this, and suspect there are some assumptions to be made which I cannot relate to. So I will not be able to do any work on this at all. What a pity.

ektanetgurl

Ok here's another clue to what I think the answer my be:
What combination of seven groups would stay the same when the goats re-grouped?
Find that and you've got the answer!
[glow=green,2,300] Think ![/glow]

ektanetgurl

one of the group numbers is ONE
that, is a hard clue but link them and THINK!!!
I won't tell anyone the answer because then it would be useless having the question.
My lips are sealed :-X

Feles_Cestriana

It is extremely impolite to chastize someone so after they ask for help.
If you wish to impress people go somewhere else. The purpose of this forum is to give people assistance.

Sir-
The issue is thusly: if each group loses one member per cycle, and the number of groups stays the same, one of the groups must consist of just one member. So, consider the following {7,6,5,4,3,2,1} this is a possible arrangement of seven groups. Now imagine the cycle: each group loses a member including the group with one; and so, youare left with {6,5,4,3,2,1,0} and the new group which has one from each, thus having seven members.... and vîola! You are back where you started...

Now if you go through and grind out the numbers, the rest should come clear... good luck, post again if you have difficulties...

      Noz Vidanyea

          Feles Cestriana