All Masks All Vessels

Combinatorial Complexity of All Masks All Vessels

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

25! = 25 x 24 x 23 x ... x 2 x 1
However, there are some restrictions:
  • Sly Vessel Fragment 1 and Sly Vessel Fragment 2 must be obtained in the exact order Sly Vessel Fragment 1 → Sly Vessel Fragment 2.
  • Sly Mask Shard 1, Sly Mask Shard 2, Sly Mask Shard 3 and Sly Mask Shard 4 must be obtained in the exact order Sly Mask Shard 1 → Sly Mask Shard 2 → Sly Mask Shard 3 → Sly Mask Shard 4.
  • Seer Vessel Fragment, and Seer Vessel Fragment must be obtained in the exact order Seer Vessel Fragment → Seer Vessel Fragment.
These restrictions reduce the total number of valid permutations.

Without restrictions, the total number of permutations would be:

25! = ~1.55 x 1025

However, due to the restrictions on the order of the Sly Vessel Fragments and Sly Mask Shards, only 1 out of every 96 permutations is valid. This is because:

  • The 2 restricted Vessel Fragments can only be obtained in one specific order, which reduces the total by a factor of 2.
  • The 4 restricted Mask Shards can only be obtained in one specific order, reducing the total by a factor of 4! = 24.
  • The 2 restricted Seer rewards can only be obtained in one specific order, reducing the total by a factor of 2.

Therefore, the total number of permutations is reduced by a combined factor of 2 x 2 x 4! = 96.

25! / (2 x 2 x 4!) = ~1.61 x 1023

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