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Algebra Level 4

In your class test, there were \(\xi \) questions. During the test, for each \(p\) satisfying \(1 \leq p \leq \xi \), \(2^{\xi -1}\) students give unexpected answers to at least \(p\) questions. If the total number of unexpected answers given is equal to \(2047,\) then what was the total number of questions in the test?

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