Can a Candidate Win Any Number of Electoral Votes from 0 to 538?

Let’s take a break from the presidential campaign to consider a recreational math question posed by New York Times correspondent Binyamin Appelbaum. On Twitter, he wondered:

Is there any number of electoral votes between 0 and 538 that is impossible to amass, assuming electors are faithful?

Put another way, could a presidential candidate win any number of electoral votes from 0 to 538?

The answer is intuitive if you know a key piece of electoral college trivia. But there’s still a fun question of how best to actually prove that intuition.

My best attempt below. Stop reading now if you want to figure it on your own.

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