who is right?

A

absoluzation

New member
Joined
Dec 4, 2019
Messages
27
The elves are nervous. Traditionally, they will personally hand over the Christmas presents to the particularly curious children in a festive ceremony this evening. Each elf has studied the list of children for a long time, and each one memorises precisely which child to give the present to. First, Santa is to hand out the gift to the most curious child in the world. After that, head elf Rebekka will give the present to the second most curious child. It continues with elf Jonathan and the present for the third most curious child, and so on.
Unfortunately, elf Eleonora has observed that Santa has spilled his cocoa on the list. Santa is embarrassed and also afraid that the elves might think he is no longer fit enough for the job. Therefore, he does not want to be helped and pretends that everything is fine. Since it is not the first time something like this has happened, elf Eleonora knows exactly how it will turn out:
Santa will simply give his gift to any child. Then, each elf who is to distribute a present afterwards will choose the right child, provided that child does not yet have a present. Otherwise, they will just randomly choose a child without a present. At the end, elf Eleonora is to hand over the last present.
Now, elf Eleonora and her best friends are puzzling over the probability that she can give her gift to the intended child. But only one elf is right. Which one?
  1. Elf Roland is positive: “As long as Santa doesn't accidentally give his present to the last child on the list, Eleonora has nothing to fear.”

  2. Elf John says: “If there were only three children on the list, the probability would be more than 1/2.”

  3. However, elf Saskia says: “Even if we knew exactly how many children are on the list this year, we can't compute it.”

  4. Elf Antje suspects: “The more children there are on the list, the smaller the probability that Eleonora can give the present to the right child.”

  5. Elf Lina replies: “Nonsense! The more children there are on the list, the greater the probability that Eleonora can give the present to the right child.”

  6. Elf Marek suspects: “We have to calculate exactly two different probabilities. One for the case that the number of children on the list is even. And one for the case that the number is odd.”

  7. Elf Nadja is pessimistic: “Eleonora should not get her hopes up... Even though the probability is constant (independent of the number of children on the list), it is less than 10 %.”

  8. Elf Kristina laughs: “I don't know what your problem is. The probability is simply 1/2.”

  9. Robert, the head of the elves' school, doesn't understand the excitement: “It's guaranteed to work.”

  10. Elf Falk is unsure: “All of your answers seem far too simple to my taste. The solution must be different.”

My answer:
Option 8 is the right one.

Santa gives his present to a random kid who corresponds to the elf in position N. For example, N is 7.
If N = 7, then that means elves 2 to 6 will give their presents to the right kids. After that, elf 7 has to give their present to
a random child. Elf 7 can only give their present to Santa's assigned kid or the elves' assigned kids with n > 7.
If they give it to Santa's assigned kid, then the last elf can give their present to the right kid.
If they give it to last elf's assigned kid, then the last elf cannot give the present to its intended target.
So basically if elf 7 gives their present to another elf's assigned kid, then the responsibility gets passed on and on.
At the end, it just depends on whether elf 7 gives their present to Santa's assigned kid or the last elf's assigned kid.
This is completely random, so that means it's 50/50. That means option 8 is the right one.

(To clarify: if Santa's kid gets a present before it's the last elf's turn then the last elf gives it to the right kid.
However, if the last elf's kid gets the present before that then the last elf has to give their present to Santa's kid -> 1/2)

Do you guys think this is a correct way of solving it? If not, can you guys help me find the right answer?
 
1) This isn't calculus at all
2) There is a forum called Math Odds & Ends for these types of puzzles to go.

It shouldn't be that difficult to post in the appropriate forum.
 
Romsek said:
1) This isn't calculus at all
2) There is a forum called Math Odds & Ends for these types of puzzles to go.

It shouldn't be that difficult to post in the appropriate forum.
Click to expand...

More importantly, are you able to answer?
 
Romsek said:
I'd say it's less importantly and crazily enough I have better things to do than figure out your brain teaser.
Click to expand...

Like bashing like you just did? You call that "having better things to do" ? That's pretty sad if you ask me.
Well, do you!
 
absoluzation said:
Like bashing like you just did? You call that "having better things to do" ? That's pretty sad if you ask me.
Well, do you!
Click to expand...
No one bashed you.

The guidelines request (quite politely) to make an effort to post in the proper forum. They also ask (again politely) to show work. Whenever you violate either rule, you waste the time of helpers, who are all VOLUNTEERS rather than your employees. Absolutely no one here is under any obligation to cater to your orders.

Try playing by the rules consistently rather than getting all huffy.
 
JeffM said:
No one bashed you.

The guidelines request (quite politely) to make an effort to post in the proper forum. They also ask (again politely) to show work. Whenever you violate either rule, you waste the time of helpers, who are all VOLUNTEERS rather than your employees. Absolutely no one here is under any obligation to cater to your orders.

Try playing by the rules consistently rather than getting all huffy.
Click to expand...

1) I mean if you clearly say you have better things to do than caring about my brain teaser then you don't need to respond at all, do you? Yes, it was a mistake of mine to put it in the wrong forum, but if you're only here to correct me about that then there literally is no need to answer at all. I hope you read "It shouldn't be that difficult to post in the appropriate forum"
2) I showed my work, didn't I? I literally asked politely whether someone could confirm my answer or not, yet I still haven't gotten any reply about that. I get that not everyone here is specialized in the kind of question I just stated, but I've literally been waiting for hours for someone to help me, and then I get that kind of response.

I'm sorry but where did I give you guys any orders? I respect every single one of you equally for taking your time to actually try solving as many problems as possible, but please I didn't visit this site to get responses like that.

And excuse me sir, but I was nowhere near being huffy in any of my messages. Please do not define me that way.
 
This is similar to the following problem.
Suppose there are 100 passengers lined up board a plane with 100 seats. Assume that 1st person on line is assigned to seat #1, the 2nd person in line is assigned to seat #2 and so on. The passengers board the plane one at a time according to their seat/position number.

The 1st person takes a random seat. Passengers #2-#99 will take their proper seat if it is vacant, otherwise they will take a random seat.

Which possible seats will be available for passenger #100 to choose from and what will be the probability of those seats being available.
 
Jomo said:
This is similar to the following problem.
Suppose there are 100 passengers lined up board a plane with 100 seats. Assume that 1st person on line is assigned to seat #1, the 2nd person in line is assigned to seat #2 and so on. The passengers board the plane one at a time according to their seat/position number.

The 1st person takes a random seat. Passengers #2-#99 will take their proper seat if it is vacant, otherwise they will take a random seat.

Which possible seats will be available for passenger #100 to choose from and what will be the probability of those seats being available.
Click to expand...

Does that mean my answer is wrong? Thank you for the example!!
 
absoluzation said:
Santa gives his present to a random kid who corresponds to the elf in position N. For example, N is 7.
If N = 7, then that means elves 2 to 6 will give their presents to the right kids. After that, elf 7 has to give their present to
a random child. Elf 7 can only give their present to Santa's assigned kid or the elves' assigned kids with n > 7.
If they give it to Santa's assigned kid, then the last elf can give their present to the right kid.
If they give it to last elf's assigned kid, then the last elf cannot give the present to its intended target.
So basically if elf 7 gives their present to another elf's assigned kid, then the responsibility gets passed on and on.
At the end, it just depends on whether elf 7 gives their present to Santa's assigned kid or the last elf's assigned kid.
This is completely random, so that means it's 50/50. That means option 8 is the right one.

(To clarify: if Santa's kid gets a present before it's the last elf's turn then the last elf gives it to the right kid.
However, if the last elf's kid gets the present before that then the last elf has to give their present to Santa's kid -> 1/2)

Do you guys think this is a correct way of solving it? If not, can you guys help me find the right answer?
Click to expand...
I just want to comment that I think your reasoning is basically right; it just isn't immediately convincing to say "random means 50/50", and you've only talked about one example. All you really need to do is to clarify that to make it a proof. That may even be what Jomo is trying to lead your toward (or else a "better" way to do it).
 
You must log in or register to reply here.
Top