How do split cards interact with brain in the jar?
When Brain in a Jar’s activated ability resolves, you can cast an instant or sorcery card with CMC equal to the number of charge counters on BiaJ for free. How this works with Split Cards is as follows: You can choose a split card if either half has a CMC equal to the number of counters, then you can cast either half of that card for free, not just the half with the matching CMC.
For example, if the second counter is put onto Brain in a Jar as its ability resolves, you can choose to cast Boom//Bust from your hand without paying its mana cost. If you do, you can cast either Boom or Bust, since the ability of Brain in a Jar only cares that the card’s CMC matches the number of counters, and Boom//Bust has a CMC of 2 while also having a CMC of 6. If you cast Bust, the fact that it doesn’t have a CMC of 2 doesn’t matter since BiaJ no longer cares about CMC at that point.
Interestingly, Brain in a Jar allows you to cast split cards with Fuse from your hand fused, as long as the CMC of one of the halves matches the number of counters on BiaJ. This is possible because you’re casting the spell from your hand, allowing it to be fused, and that Fuse isn’t an alternate cost but rather a choice you can make to cast both halves of the spell instead of just one or the other.
(If Fuse were an alternate cost, then it would clash with casting the spell for free as you can only pay one alternate cost to cast a spell, but it’s not, so it doesn’t.)
For example, if you put the second counter on BiaJ as its ability resolves, you can choose to cast Breaking//Entering from your hand and cast either Breaking, Entering, or both halves fused.