an​ orchestra, 23 people can play stringed​ instruments, 21 can play​ brass, and 15 can play percussion.​ Further, 9 of the performers can play both strings and​ brass, whereas 8 can play both strings and percussion. If no one can play all three types of​ instruments, what are the maximum and minimum numbers of people in the​ orchestra? ​(Hint. Consider expressing the numbers in some of the regions of your diagram in terms of a single​ unknown, say​ x.)

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