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24 May 2021, 15:16
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A teacher wants to distribute books among his students, and has 11 math, 13 biology and 17 history students. If the teacher gives all students the same highest number of books, he will still have some books remaining. The same happens if he tries to distribute the books among only two groups of students: math/biology, math/history or biology/history students. If he tries to distribute the books among only math, biology or history students, the following numbers of books will be left: 1, 8 or 3, respectively. The teacher eventually decides to give each student the same maximal number of books, and give the rest to his brother. What is the minimum number of books the teacher could have had that fit this scenario?
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