Solving for two unknowns when filing in two states

[niccolo]

Tax conundrum: During 2013, I maintained my permanent residence in CA and was a part-year resident in DC. Both states allow me to deduct a portion of the tax I paid to the other. But I can't calculate how much tax I owe to each without knowing how much tax I owe to the other. My tax program provides no useful way to address this "solve for two unknowns simultaneously" problem, but lots of other people must have the exact same problem and must solve it without hardcore calculus or hundreds of iterations to gradually home in on the right answer. Am I missing something? Assistance appreciated!

 

[kirby]

You deduct the tax actually paid in 2013 for both states. So you already know both numbers