Six maths students, Amy, Bao, Cecil, Daria, Emilia and Felipe are given 60 problems to complete over the weekend. Although none of them completes all 60, each completes at least 52 of the problems, and each one completes a different number of problems. Also the order from least to most problems is the same as the alphabetical order of their names. Finally, each of them completes 𝑘 times as many problems on Saturday as they do on Sunday, where 𝑘 is a different whole number from 1 to 6 for each of them.Which of them completed 3 times as many problems on Saturday as on Sunday?
Question
Six maths students, Amy, Bao, Cecil, Daria, Emilia and Felipe are given 60 problems to complete over the weekend. Although none of them completes all 60, each completes at least 52 of the problems, and each one completes a different number of problems. Also the order from least to most problems is the same as the alphabetical order of their names. Finally, each of them completes 𝑘 times as many problems on Saturday as they do on Sunday, where 𝑘 is a different whole number from 1 to 6 for each of them.Which of them completed 3 times as many problems on Saturday as on Sunday?
Solution
To solve this problem, we need to consider the constraints given:
- Each student completes at least 52 problems but not all 60.
- The number of problems each student completes is different.
- The order of the number of problems completed is the same as their alphabetical order.
- Each student completes k times as many problems on Saturday as they do on Sunday, where k is a different whole number from 1 to 6 for each of them.
Given these constraints, we can start by assigning the minimum number of problems (52) to Amy, since she is first in alphabetical order. We then assign 53 problems to Bao, 54 to Cecil, 55 to Daria, 56 to Emilia, and 57 to Felipe.
Next, we need to determine the value of k for each student. Since Amy completed the least number of problems, she must have completed 1 times as many problems on Saturday as on Sunday. Bao must have completed 2 times as many problems on Saturday as on Sunday, Cecil 3 times, Daria 4 times, Emilia 5 times, and Felipe 6 times.
Therefore, the student who completed 3 times as many problems on Saturday as on Sunday is Cecil.
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