Weihnachtsmann rot

Challenge from 21. December

Xmasium

Authors: Cor Hurkens, Frits Spieksma

Project: 4TU.AMI

Challenge:

In one of Santa Claus' research laboratories the scientists have discovered a new chemical element and named it Xmasium (in analogy with the famous elements Rubidium, Caesium and Francium). Every Xmasium atom consists of several fermions, bosons, and other elementary particles. Cutting edge breakthrough research has shown that Xmasium atoms show up in two fundamentally different types: there are Xmasium atoms with a Higgs boson, and there are Xmasium atoms without a Higgs boson. With the currently available lab equipment, it is not possible to distinguish the two types from each other.

Xmasium atoms possess some rather interesting properties:

  • If you throw an Xmasium atom A with Higgs-boson against an Xmasium atom B without Higgs boson, the Higgs boson is separated from atom A and snuggles up to atom B. In other words, both Xmasium atoms change their type.

  • In the other three cases (A and B with Higgs boson; A and B without Higgs boson; A without and B with Higgs-boson) such a throw remains without consequences, and both atoms keep their old type.

The transmission of a Higgs boson occurs lightning-fast and cannot be observed with the available lab equipment.

Ruprecht has six Xmasium atoms X1, X2, X3, X4, X5, and X6 of unknown type in his cooking pot. Ruprecht would like to brightly polish two atoms of the same type, put them into a gift box, and give them to Santa Claus as a present. (The other four atoms will remain in the cooking pot.)

What is the least number of throws that Ruprecht has to perform in the worst case, so that he ends up with at least two atoms of the same type?

Artwork: Frauke Jansen

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Possible answers:

  1. In the worst case, Ruprecht needs 2 throws.

  2. In the worst case, Ruprecht needs 3 throws.

  3. In the worst case, Ruprecht needs 4 throws.

  4. In the worst case, Ruprecht needs 5 throws.

  5. In the worst case, Ruprecht needs 6 throws.

  6. In the worst case, Ruprecht needs 8 throws.

  7. In the worst case, Ruprecht needs 10 throws.

  8. In the worst case, Ruprecht needs 12 throws.

  9. In the worst case, Ruprecht needs 15 throws.

  10. In the worst case, Ruprecht is not able to achieve this goal.

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