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There are an infinite number of possible answers:

1 + 123, 2 + 122, 3 + 121 etc

then

1.1 + 122.9, 1.2 + 122.8 etc

and

1.01 + 122.99, 1.02 + 122.98 etc

And then you could include negative numbers:

125 - 1, 126 - 2, etc

and also irrationals: 1+sqrt(2), 123-sqrt(2), etc

etc

And that is only pairwise addition. You could add 3, 4, 5 ... an infinite number of numbers!

Edit: If you mean whole numbers (excluding integers and all that other junk), then... do you mean how many pairs of numbers add up to 124?

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Q: What numbers add up to 124?
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