"There are 57 students. 18 Greek, 13 Finns, 6 Russians and 20 Swedes. The students study in groups. A group always consists of one or more students. If a group has at least 2 students that are of same nationality, then the group has to have at least one student who is different nationality. How many different ways are there to divide the 57 students to groups?"

Question

wmj259 · Answer

Is there a limit to how many total groups can be made?

tanya123 · Answer

The maximum is 57. So one way to divide the groups would be to either have only one 57 people group or even 57 one-person groups.

anonymous · Answer

That's correct, those are two possibilities

anonymous · Answer

I'm hoping you didn't stop there...

tanya123 · Answer

I think your question is kinda incomplete for some reason

anonymous · Answer

It is not. The final solution will have like 20 digits or something. But that is indeed the question in its entirety

deadly_roses · Answer

so this question is saying that for every 2 students of the same nationality there is 1 from another? because it says that: "If a group has at least 2 students that are of same nationality, then the group has to have at least one student who is different nationality."

anonymous · Answer

Yes, you should take that into consideration as well

anonymous · Answer

The school doesn't want students from the same country being alone together I guess

deadly_roses · Answer

okay the most groups we can make is: 57 if they are just one person.....but this is asking for the amount of ways to divide it right?

anonymous · Answer

Yes, indeed. It will be a ridiculous amount

deadly_roses · Answer

true...let me get a paper...and i will figure it out...i think i know how i need to do it...

anonymous · Answer

You are a true pro if you can nail this one

anonymous · Answer

Oh, but I just saw you're only 15 years old... I am afraid this requires quite complex math

deadly_roses · Answer

okay this is actually not that hard...it is a tedious problem but it can be solved....when dividing 57 you can divide it by 1 but not 2 divide by 3 but not 4...only odd numbers can be divided....and that works because 1) the way the groups are set it that for every 2 from the same country you have 1 equaling 3 an odd number....the groups cant be divided very much actually...to solve the problem you just have to figure out how many odd numbers you can divide from the 57 and get an even number for your answer...

deadly_roses · Answer

if that makes any sense....

anonymous · Answer

You can also have a group of 18 Greeks and 1 Russian... Or 18 Greeks and 6 Russians

deadly_roses · Answer

well itsnt it for every 2 of the nationality that you would have 1 from another... so it wasnt be 18 Greeks and 1 Russian...it would have to be 9 pairs of 2 Greeks with 6 Russians and 2 swedes....so that they all matched up according to the set up of groups...

deadly_roses · Answer

same*

anonymous · Answer

That's incorrect