One of Professor Marina’s classes has 30 students enrolled. One day, to do a class activity, she planned to form groups with the same number of students.
However, Marina pointed out that not everyone was present that day and that:
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If only pairs were formed, one student would be alone.
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if there were only trios, a student would be alone.
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could divide the class into quintets only.
How many students were absent that day?
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Solution:
That day, five students were absent.
Find this riddle and others on the Obmep portal (Brazilian Public School Mathematics Olympiad) organized by Impa (Institute of Pure and Applied Mathematics).
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