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Consider: There are three balls: one is 1kg, another is 3kg, and the other is 5kg.

I am trying to describe the ball of 3kg in a complicated way as follows:

I need one ball other than/different from the two balls that have a difference of weight greater than 2kg.

I would like to know "other than" or "different from" which is correct for the sentence.

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As per Collins English Dictionary - You use other than after a negative statement to say that the person, item, or thing that follows is the only exception to the statement e.g. She makes no reference to any feminist work other than her own.

Whereas the adjective different means ‘not the same’. When we compare two or more items, it is usually followed by from. We also use different to, especially in speaking e.g. Adam is so different from/to his brother.

Thus "other than" should be for the sentence.

I need one ball other than from the two balls that have a difference of weight greater than 2kg.

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    I don't think you intended the from in that sentence, Sri9911.
    – Colin Fine
    Feb 23, 2020 at 11:13
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This is not natural nor understandable.

In the context you give the fact that the middle ball is 3kg is easily worked out by the speaker, so you would say:

I need a 3 kg ball.

You would not try to find a more complicated way of expressing this simple idea.

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