Weihnachtsmann rot

Challenge from 14. December

Clumsy Santa is Coming to Town
  • There at least two children on the list.

  • Eleonora always gives the present to the last child on the list (if necessary, the elves before Eleonora will be left out).

Authors: Luise Fehlinger, Thilo Steinkrauß

Project: Berliner Netzwerk mathematisch-naturwissenschaftlich profilierter Schulen

Challenge:

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?

Artwork: Friederike Hofmann

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Possible answers:

  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.”

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Project relevance:

The Berliner Netzwerk mathematisch-naturwissenschaftlich profilierter Schulen has existed since September 2001 and has set the following goals:

  • Creating a city-wide network of Berlin high schools with an existing or future profile and the mathematics in mathematics and science with the institutes of Humboldt-Universität at the campus Adlershof.

  • Establishing standards for advanced courses (Leistungskurse) in mathematics and the other participating natural science subjects that enable the recognition of Abitur achievements as academic credits.

The Senator for Education, Youth and Family Affairs and the university administration of Humboldt-Universität welcome and support this project. For the future, we also envision a high school with a mathematics and natural sciences profile located at the science and business campus Adlershof, which is strongly connected to the institutes of Humboldt-Universität.