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Omni-MATH / Another professor enters the same room and says, 'Each of you has to write down…

Problem

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problem

Another professor enters the same room and says, 'Each of you has to write down an integer between 0 and 200. I will then compute XX, the number that is 3 greater than half the average of all the numbers that you will have written down. Each student who writes down the number closest to XX (either above or below XX) will receive a prize.' One student, who misunderstood the question, announces to the class that he will write the number 107. If among the other 99 students it is common knowledge that all 99 of them will write down the best response, and there is no further communication between students, what single integer should each of the 99 students write down?
Plain-text mathematical notation (without MathML)
Another professor enters the same room and says, 'Each of you has to write down an integer between 0 and 200. I will then compute X, the number that is 3 greater than half the average of all the numbers that you will have written down. Each student who writes down the number closest to X (either above or below X) will receive a prize.' One student, who misunderstood the question, announces to the class that he will write the number 107. If among the other 99 students it is common knowledge that all 99 of them will write down the best response, and there is no further communication between students, what single integer should each of the 99 students write down?
Original LaTeX notation
Another professor enters the same room and says, 'Each of you has to write down an integer between 0 and 200. I will then compute $X$, the number that is 3 greater than half the average of all the numbers that you will have written down. Each student who writes down the number closest to $X$ (either above or below $X$) will receive a prize.' One student, who misunderstood the question, announces to the class that he will write the number 107. If among the other 99 students it is common knowledge that all 99 of them will write down the best response, and there is no further communication between students, what single integer should each of the 99 students write down?

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Source and history

task_id
7ecc9a1a-8c46-5033-8e2e-5ef238b48d25
task_key
test--7ecc9a1a-8c46-5033-8e2e-5ef238b48d25
task_revision_id
1
config / split
/ test

Official source

initial import