16 Mask Shards

Combinatorial Complexity of 16 Mask Shards

When randomizing the order of obtaining 16 Mask Shards, the number of possible unique permutations is given by:

16! = 16 x 15 x 14 x ... x 2 x 1

Sly Mask Shard 1, Sly Mask Shard 2, Sly Mask Shard 3 and Sly Mask Shard 4 have specific restrictions. They must be obtained in the exact order Sly Mask Shard 1 → Sly Mask Shard 2 → Sly Mask Shard 3 → Sly Mask Shard 4. This restriction reduces the total number of valid permutations.

Without restrictions, the total number of permutations would be:

16! = 20,922,789,888,000

However, due to the restrictions on the order of the Sly Mask Shards, only 1 out of every 24 permutations is valid, which reduces the total number of permutations by a factor of 4! = 24.

16! / 4! = 871,782,912,000

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