# Elves

#### absoluzation

##### New member
So my teacher told me to solve this problem, but I'm not sure if I did it the right way... I love math but this is like the hardest question I've ever been asked.
Anyone interested in helping? It would mean a lot!

The question:

For their good work today, the five sneaky elves Charlie, Kim, Luca, Mika, and Ulli received big box with finitely many, whole, delicious coconut macaroons from Santa himself. Worn out from the exhausting day, they carry the box home and go to bed immediately while yawning loudly. Now, the box sits on the elves' kitchen table, where it is guarded by the elves' dog Anouk.

At 10:34 p.m., Charlie sneaks into the kitchen, gives a macaroon from the box to Anouk, divides the remaining macaroons into five equal parts (while not dividing a single macaroon), pouches one part, rearranges the residual four parts into a big pile, and returns to bed with a cunning grin on the face. At 11:56 p.m., Kim tiptoes into the kitchen, gives a macaroon from the box to Anouk, divides the remaining macaroons into five equal parts (without splitting single macaroons), puts one of theses parts into the pyjama pockets, shoves the other four parts into a pile, and slips off to bed looking very pleased. At 1:45 a.m., 3:17 a.m., and 4:23 a.m., Luca, Mika, and Ulli, respectively, repeat this procedure.

Despite the wakeful night, the elves are in a very good mood at 9:00 a.m. and meet for breakfast. They offer a breakfast macaroon to Anouk and split the remains of the coconut macaroons equally among themselves (again, dividing none of the single macaroons).

How many coconut macaroons does Kim at least get altogether?

#### Subhotosh Khan

##### Super Moderator
Staff member
So my teacher told me to solve this problem, but I'm not sure if I did it the right way... I love math but this is like the hardest question I've ever been asked.
Anyone interested in helping? It would mean a lot!

The question:

For their good work today, the five sneaky elves Charlie, Kim, Luca, Mika, and Ulli received big box with finitely many, whole, delicious coconut macaroons from Santa himself. Worn out from the exhausting day, they carry the box home and go to bed immediately while yawning loudly. Now, the box sits on the elves' kitchen table, where it is guarded by the elves' dog Anouk.

At 10:34 p.m., Charlie sneaks into the kitchen, gives a macaroon from the box to Anouk, divides the remaining macaroons into five equal parts (while not dividing a single macaroon), pouches one part, rearranges the residual four parts into a big pile, and returns to bed with a cunning grin on the face. At 11:56 p.m., Kim tiptoes into the kitchen, gives a macaroon from the box to Anouk, divides the remaining macaroons into five equal parts (without splitting single macaroons), puts one of theses parts into the pyjama pockets, shoves the other four parts into a pile, and slips off to bed looking very pleased. At 1:45 a.m., 3:17 a.m., and 4:23 a.m., Luca, Mika, and Ulli, respectively, repeat this procedure.

Despite the wakeful night, the elves are in a very good mood at 9:00 a.m. and meet for breakfast. They offer a breakfast macaroon to Anouk and split the remains of the coconut macaroons equally among themselves (again, dividing none of the single macaroons).

How many coconut macaroons does Kim at least get altogether?
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#### Dr.Peterson

##### Elite Member
This is a variation of a very famous problem. (I won't tell you what beings are involved in the usual versions, so you can't just look it up.) It can be solved in a couple different ways, any of which for you probably will involve some creativity. Yes, it is hard, and the numbers involved get very large!

Give it a try, so we can see what ideas you have about it, and we can see if we can guide you along the way. I wouldn't want to spoil the fun of discovery by giving away too much.

#### absoluzation

##### New member
This is a variation of a very famous problem. (I won't tell you what beings are involved in the usual versions, so you can't just look it up.) It can be solved in a couple different ways, any of which for you probably will involve some creativity. Yes, it is hard, and the numbers involved get very large!

Give it a try, so we can see what ideas you have about it, and we can see if we can guide you along the way. I wouldn't want to spoil the fun of discovery by giving away too much.
So basically what I did was create a formula for Charlie: (x-1)/5 - 1/5*(x-1)/5 --> (4x-4)/25
Then I made one for the other people involved.
Kim: (3x-3)/25
Luca: (2x-2)/25
Mika: (x-1)/25

So then I tried finding x but x always equals 1 here.

After this I got completely lost.. It would mean a lot if you helped!

a=bq+r.
r=remainder
a=dividend
b=divisor
q=quotient
Now try.

#### Dr.Peterson

##### Elite Member
So basically what I did was create a formula for Charlie: (x-1)/5 - 1/5*(x-1)/5 --> (4x-4)/25
Then I made one for the other people involved.
Kim: (3x-3)/25
Luca: (2x-2)/25
Mika: (x-1)/25

So then I tried finding x but x always equals 1 here.

After this I got completely lost.. It would mean a lot if you helped!
The first thing to do is to make sure you're interpreting everything right; then you can start actually solving. Here are the important bits of the problem:
• Charlie gives a macaroon to Anouk, divides the remaining macaroons into five equal parts, takes one part, rearranges the residual four parts into a big pile.
• Kim gives a macaroon to Anouk, divides the remaining macaroons into five equal parts, takes one of these parts, shoves the other four parts into a pile.
• Luca, Mika, and Ulli, respectively, repeat this procedure.
• They offer a macaroon to Anouk and split the remains of the macaroons equally among themselves.
Your expression for what Charlie leaves (assuming that's what you mean) is close, but you seem to have him dividing the pile into 5 twice. I'd say he just takes 1/5 and leaves 4/5 of x-1.

Then you have each of the others taking more than 1/5; and you don't have their actions starting with what the previous one left. Isn't x the original amount in the pile? Or is your x different for each of them? (If so, that's not good.)

Then, of course, you missed Ulli and the final meeting.

So, keep working until you get an accurate mathematical model of what is happening, and then we can try to solve it. And that solving, too, will require your ideas; this is not a routine problem, so you'll have to think about ways to solve it.

#### absoluzation

##### New member
The first thing to do is to make sure you're interpreting everything right; then you can start actually solving. Here are the important bits of the problem:
• Charlie gives a macaroon to Anouk, divides the remaining macaroons into five equal parts, takes one part, rearranges the residual four parts into a big pile.
• Kim gives a macaroon to Anouk, divides the remaining macaroons into five equal parts, takes one of these parts, shoves the other four parts into a pile.
• Luca, Mika, and Ulli, respectively, repeat this procedure.
• They offer a macaroon to Anouk and split the remains of the macaroons equally among themselves.
Your expression for what Charlie leaves (assuming that's what you mean) is close, but you seem to have him dividing the pile into 5 twice. I'd say he just takes 1/5 and leaves 4/5 of x-1.

Then you have each of the others taking more than 1/5; and you don't have their actions starting with what the previous one left. Isn't x the original amount in the pile? Or is your x different for each of them? (If so, that's not good.)

Then, of course, you missed Ulli and the final meeting.

So, keep working until you get an accurate mathematical model of what is happening, and then we can try to solve it. And that solving, too, will require your ideas; this is not a routine problem, so you'll have to think about ways to solve it.
I still don't get it sir :/ Thanks for helping though..

#### absoluzation

##### New member
a=bq+r.
r=remainder
a=dividend
b=divisor
q=quotient
Now try.
Oh hi again! Can you tell me how to do it?

#### Dr.Peterson

##### Elite Member
The goal here is for you to do some work, and we try to help you learn to solve problems yourself.

You don't appear to be making any effort, so I'm out.

#### absoluzation

##### New member
The goal here is for you to do some work, and we try to help you learn to solve problems yourself.

You don't appear to be making any effort, so I'm out.
Excuse me? I've literally been working on this for the PAST 5 HOURS trying to find a solution. How am I supposed to learn when I don't even know where to start? I don't even get your explanation. "You don't appear to be making any effort" I'm sorry mister know it all but some people aren't good at solving problems, yet I'm still trying. Only claim things when you know the background.

I didn't need your help. Your explanation was whack anyways. Later.

#### Dr.Peterson

##### Elite Member
You didn't show any effort, beyond the first attempt that I tried to help you with. Your response was only "I still don't get it", and then "Can you tell me how to do it?", without any additional information to help me respond. I took that to mean that you just wanted to be given an answer.

If that's not what you meant, then by all means show some more work, or else tell me what you didn't understand that I said, and we can try to provide some help.

#### Jomo

##### Elite Member
Excuse me? I've literally been working on this for the PAST 5 HOURS trying to find a solution. How am I supposed to learn when I don't even know where to start? I don't even get your explanation. "You don't appear to be making any effort" I'm sorry mister know it all but some people aren't good at solving problems, yet I'm still trying. Only claim things when you know the background.

I didn't need your help. Your explanation was whack anyways. Later.
absoluzation, Dr Peterson by far is the nicest helper on this forum. I can understand how you felt when Dr Peterson said that I'm out. Trust me, Dr Peterson did not mean anything bad by this. He really thought that you just wanted the answer.
Please work with him and if you do not understand any he says, then please tell him. On this forum we put the students first and we know that just giving out answers does not work. We prefer to help you get the solution on your own with our assistance. Please post some of your work so we can tell you what is correct and what is not. Thank you.

#### firemath

##### Junior Member
You didn't show any effort, beyond the first attempt that I tried to help you with. Your response was only "I still don't get it", and then "Can you tell me how to do it?", without any additional information to help me respond. I took that to mean that you just wanted to be given an answer.

If that's not what you meant, then by all means show some more work, or else tell me what you didn't understand that I said, and we can try to provide some help.
Some respectful context:
He's Dutch, and he is having a hard time communicating in our math terms.

#### Dr.Peterson

##### Elite Member
I perhaps was a little hasty or harsh in what I said, but at this point I'm just waiting for more information about what is needed, or another attempt at writing equations. Until I see that, there's not much more I can do to help.

Would it help if I add that this kind of problem is often expressed in terms of monkeys and coconuts?

#### firemath

##### Junior Member
I perhaps was a little hasty or harsh in what I said, but at this point I'm just waiting for more information about what is needed, or another attempt at writing equations. Until I see that, there's not much more I can do to help.

Would it help if I add that this kind of problem is often expressed in terms of monkeys and coconuts?
I helped him with it on MHF. He asked the question there, too. I gave him the formula. We'll see how he does.

#### absoluzation

##### New member

I helped him with it on MHF. He asked the question there, too. I gave him the formula. We'll see how he does.

Yeah you did give me the formula but I don't know what words like "remainder" mean so I wasn't really able to solve anything.

#### absoluzation

##### New member
I perhaps was a little hasty or harsh in what I said, but at this point I'm just waiting for more information about what is needed, or another attempt at writing equations. Until I see that, there's not much more I can do to help.

Would it help if I add that this kind of problem is often expressed in terms of monkeys and coconuts?
I'm sorry I thought you were "out". You don't need to be here. I want anyone to help me but you. Please be kind to leave this thread.

#### firemath

##### Junior Member

Yeah you did give me the formula but I don't know what words like "remainder" mean so I wasn't really able to solve anything.
Abosoluzation, I explained the word remainder to you on MHF. After I did, you said that you needed to expand your English vocabulary and that I could explain it in "math speak." I do not understand why you are making this more difficult than it needs to be.

I am not angry, but I don't like to be told that I didn't help when I did.
I still want to help you, but I do not want to help if you will not do your part.
And please be kind to Dr. Peterson. He is a brilliant man whom you have no right to be harsh with.

#### absoluzation

##### New member
Abosoluzation, I explained the word remainder to you on MHF. After I did, you said that you needed to expand your English vocabulary and that I could explain it in "math speak." I do not understand why you are making this more difficult than it needs to be.

I am not angry, but I don't like to be told that I didn't help when I did.
I still want to help you, but I do not want to help if you will not do your part.
And please be kind to Dr. Peterson. He is a brilliant man whom you have no right to be harsh with.
I never said you didn't help, did I?
I know you explained it to me but I still don't get it.

Do you have any idea what it feels like to be called someone that doesn't put any effort when I've literally been working on this for a day.

I don't need to show you my progress because
1. You guys are just gonna tell me what I did wrong, not what I should be doing next.
2. You guys will call me lazy over nothing.

Forget about this thread. You are all just being toxic. I will visit some other forums.

#### Dr.Peterson

##### Elite Member
Oh well. If this thread had continued, I would have eventually mentioned a hint that makes it almost easy; unfortunately, it can only be used when you have reached a certain point in understanding the problem. But it's much more satisfying than just being given a formula that someone else worked out. (I didn't invent it, but was very happy when I was told it 20 years ago and realized how it worked.)

For the sake of anyone who might be interested, here it is: imagine there is a plate with 4 extra macaroons sitting in the room, which remains untouched throughout the story. Then keep track of the total number of macaroons present at each step, including these four. Complicated calculations become a whole lot simpler.