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If the capital city of a US state conforms to a special rule, I identify it as having a Balanced State of Capital™. As it turns out, only 8 of the 50 state capitals qualify for this Balanced State.

Those 8 state capitals, in alphabetical order, are:

  • Atlanta, GA
  • Boise, ID
  • Juneau, AK
  • Nashville, TN
  • Phoenix, AZ
  • Richmond, VA
  • Sacramento, CA
  • Topeka, KS

What rule defines these each as Balanced State of Capitals?

Hint 1:

There are 42 state capitals that don't qualify. Look at a few to see how they might differ from these.

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A capital city has a Balanced State of Capital if

it has the same number of letters in its name as its respective state.

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