A class with 2N students took a quiz, on which the possible scores were
0, 1, . . . , 10. Each score appeared at least once.
The average score for this class was exactly 7.4.
Show that the class can be divided into two groups of N members each, such that that the average score for each group was exactly 7.4.
I think I was overcomplicating it! Following my original strategy, since the associated pairs of numbers in the two groups will always differ by at most 1, you can just swap however many pairs you need that differ by one each to make the sums of the two groups equal. (No need to find a single pair with the exact difference you need, which for some reason is where my mind was stuck for a while.)
In my illustration of Larry's example, just swap any three of the six pairs that differ by one to make the two groups equal.
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Posted by tomarken
on 2024-02-24 14:54:00 |
Duh
