A new element!

Dec 2019
52
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In one of Santa's research laboratories, the scientists have discovered a new chemical element and have named it Xmasium (by analogy with the famous elements Rubidium, Caesium, and Francium). Xmasium exists in three different types: There is α-Xmasium, β-Xmasium, and γ-Xmasium. If two Xmasium-atoms of different type collide, they sometimes merge into a single atom of the third type. If two Xmasium-atoms of the same type collide, they repel each other and nothing else happens.

Ruprecht puts 91 α-Xmasium-atoms, 25 β-Xmasium-atoms, and 4 γ-Xmasium-atoms into a cooking pot, covers it, and then leaves for lunch. When he returns, he notices that all Xmasium-atoms in the pot now are of the same type.

What is the largest possible number z of Xmasium-atoms in the pot at that moment?

  1. This largest possible number satisfies 20 ≤ z ≤ 23.

  2. This largest possible number satisfies 24 ≤ z ≤ 27.

  3. This largest possible number satisfies 28 ≤ z ≤ 31.

  4. This largest possible number satisfies 32 ≤ z ≤ 35.

  5. This largest possible number satisfies 36 ≤ z ≤ 39.

  6. This largest possible number satisfies 40 ≤ z ≤ 43.

  7. This largest possible number satisfies 44 ≤ z ≤ 47.

  8. This largest possible number satisfies 48 ≤ z ≤ 51.

  9. This largest possible number satisfies 52 ≤ z ≤ 55.

  10. This largest possible number satisfies 56 ≤ z ≤ 59.