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Invested metals


Dawnshard

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There are 16 Allomantic metals and 16 shards. However in Rhythm of War we see Warlight. A combination of Honor and Odium's light. So how many total metal combinations are there? I suck at math. Also I am assuming there can be combinations of three or more shards to create a new light. Also I think you can condense light into a metal. So how many metals can a Mistborn Burn, if a Mistborn burns all metals. (How much wood can a woodchuck chuck, if a woodchuck could chuck wood?)

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There are 16C2 combinations of 2 shards out of a pool of 16 => 16 * 15 / 2 (16 shards to pick for the first, 15 other shards to pick from the second, but since e.g. Honor-Odium is the same as Odium-Honor, need to account for the double counting) = 120.

There are 2^16 - 1 (65535) combinations of 1 or more shards given the pool of 16 (for each shard, we can decide whether or not to add it to the pool, or 2 choices per shard, so 2 * 2 * ... * 2 16 times, minus the 1 'empty' choice where we don't add any shard).

It's unclear if there's a direct relationship between Allomantic metals and the shards, besides the number. 

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