My solution involves assigning a different prime number to each letter "a" to
"z" (and the same prime numbers to the capital letters). Then assign a value to
each state as the product of the primes corresponding the letters in the state
name.
Then a pair of states can be rearranged into another pair if and only if the
product of the values assigned to the first pair equals the product of the
values assigned to the second pair.
So create a table of all possible such products, each product associated with a
list of pairs. Then any list which contains more than one pair gives a solution.
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