Weihnachtsmann rot

Challenge from 23. December

Sea of Lights

Tomorrow's challenge will already be published at 10am (CET).

Author: Ariane Beier

Project: MATH+ School Activities


Finally! Tomorrow is Christmas Eve. Accordingly, the elves have almost finished their Christmas preparations: they baked biscuits, made presents, and put up and decorated the Christmas tree in the festival hall. Now, all that's left to be done is decorating Main Street in Elf Town. To do this, head elf Omega instructs elf Epsilon to put up 2020 lights along the street.

Epsilon sets off and completes her task in almost no time. All of the 2020 lights shine brightly. After her work is done, she is about to treat herself to a delicious speculoos and a nice hot cocoa when Gamma approaches her frantically: “Epsilon, you forgot to label the switches on the big control panel in the basement. If we don't know which switch belongs to which light, we won't be able to perform our choreography of lights tomorrow evening. So, hurry up! Go down to the basement and label the control panel!”

In her mind, Epsilon can already see herself running back and forth between the street and the control panel in the basement for the next few hours, in order to assign all 2020 lights to all 2020 switches without ambiguity—while her cocoa is slowly but surely getting cold. However, while she takes the last motivating sip from her cup, she has an idea how to minimise the number m of ways to the basement that are required to fulfil her task.

Which statement about this minimal number m is true?

Artwork: Frauke Jansen

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Possible answers:

  1. m ≤ 12.

  2. 12 < m ≤ 42.

  3. 42 < m ≤ 63.

  4. 63 < m ≤ 173.

  5. 173 < m ≤ 196.

  6. 196 < m ≤ 308.

  7. 308 < m ≤ 712.

  8. 712 < m ≤ 1608.

  9. 1608 < m ≤ 1984.

  10. 1984 < m ≤ 2019.

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