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Dawnshard

Invested metals

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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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Theoretically infinate we have 16 allomantic metals 16 shard metals, silver has some properties, Dragonsteel, alloys alloys between them and Combining Shards makes new metals

MB

Spoiler

Ettmetal is not the same as a Atium Lerasium alloy

 

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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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Additionally proportions matter in alloys

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