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Omni-MATH / Reading from left to right, a sequence consists of 6 X's, followed by 24 Y's,…

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problem

Reading from left to right, a sequence consists of 6 X's, followed by 24 Y's, followed by 96 X's. After the first nn letters, reading from left to right, one letter has occurred twice as many times as the other letter. What is the sum of the four possible values of nn?
Plain-text mathematical notation (without MathML)
Reading from left to right, a sequence consists of 6 X's, followed by 24 Y's, followed by 96 X's. After the first n letters, reading from left to right, one letter has occurred twice as many times as the other letter. What is the sum of the four possible values of n?
Original LaTeX notation
Reading from left to right, a sequence consists of 6 X's, followed by 24 Y's, followed by 96 X's. After the first \(n\) letters, reading from left to right, one letter has occurred twice as many times as the other letter. What is the sum of the four possible values of \(n\)?

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