All Charm Notches

Combinatorial Complexity of All Charm Notches

When randomizing the order of obtaining All Charm Notches, the number of possible unique permutations is given by:

10! = 10 x 9 x 8 x ... x 2 x 1
However, there are some restrictions:
  • Salubra Notch 1, Salubra Notch 2, Salubra Notch 3 and Salubra Notch 4 must be obtained in the exact order Salubra Notch 1 → Salubra Notch 2 → Salubra Notch 3 → Salubra Notch 4. Although this is not necessary, it will make charm collecting more convenient.
  • Grimmchild, Grimmchild Lvl 2 and Grimm Notch must be obtained in the exact order Grimmchild → Grimmchild Lvl 2 → Grimm Notch. Grimmchild is added to make the race more interesting.

Without restrictions, the total number of permutations would be:

10! = 3,628,800

However, due to the restrictions on the order of the Notch Salubra and Grimmchild elements, only 1 out of every 576 permutations is valid. This is because:

  • The 4 restricted Notch Salubra elements can only be obtained in one specific order, which reduces the total by a factor of 4! = 24.
  • The 3 restricted Grimm elements can only be obtained in one specific order, reducing the total by a factor of 3! = 6.

Therefore, the total number of permutations is reduced by a combined factor of 4! x 3! = 24 x 6 = 576.

10! / (4! x 3!) = 25,200

Built by Marclap. The source code is available on Github.