[High School Math] Problem of the Week, was said to be impossible by some classmates.

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morroblivion is in High School Math

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The full statement/question

"There are 18 students in a class. Everyday 3 students are scheduled to attend the class. It was found that every pair of students had met in class together exactly once. How many days did the class last?"

2 guys who excelled in math said there is no answer / impossible. One of them reasoned:

"I too think it's impossible because if you have 18 elements and you're trying to group them by threes with each possible pair occurring only once, ABC | ADE | AFG | AHI | AJK | ALM | ANO | APQ | AR, there's one element () that would have to repeat making this pair (A_) repeat. If there were 4 elements (A,B, C, D), it would be impossible because on one day you can have ABC and the next day it will be ABD/ADC/DBC one of the pairs in the first day (AB/AC/BC)."

so, is this answereable or not?

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morroblivion

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Posted: 11 years ago
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