Unfortunately, either answer is correct. If this is from a reading exercise you MUST show us the context. There are two different meanings here.
A. others = other children,but not all the other children
B. the others = all the other children
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Here you better say:
"Some are reading, some are writing..."
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many children in the classroom. some are reading, __B.the others__are writing. (A.others B.the others)