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If I want to say that 2 (or more) balls have the same size, I say:

they have the same size

But is it also correct to say this?

they have the same sizes

If it is, when would you use it like this?

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    They are the same size. If you are talking about more than two items then I would say, "they are all the same size." If they are not the same then it's, "they are different sizes." – Joe Dark Sep 19 '15 at 18:35
  • Good point, "are the same size" sounds better. Just out of curiosity is "have the same size" totally wrong or just unnatural/worse? – Andrew Sep 19 '15 at 22:23
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The phrases

the same size

and

the same sizes

both have the right to exist, and are used to mean different characteristics of the objects which they describe.

If a class of objects can be dimensioned in two or more of ways, for example, pipe segments have the outer (or inner) diameter, wall thickness and the length, then, comparing two pipe segments, you can say

Those two segments have the same sizes.

if you mean that all dimensions of the two objects measure equal to each other (within some tolerance).

If in some context only specific dimension (like length, for instance) is deemed important, and other dimensions can be ignored, you can say about two pipe segments of two diameters

Those two segments have the same size.

if their length is what's currently important.

When talking of items of clothing, you can say of different pairs of shoes that they all have the same size, although no dimension of those complex shapes is the same if carefully measured: the shoe "size" is a marking, classifier, which is only approximately associated with a certain dimension.

Back to your example...

A filled sphere (a ball) has essentially only one dimension - the diameter. Often enough it is a hollow sphere, and the wall thickness can be taken as the other dimension, but if it is a solid sphere, there is no other dimension. This way when you only compare one dimension, it is more natural to use singular. But it would not be wrong to say

The diameters of those balls are [all] the same.
They have the same diameters.

Phrase "the same" when describing a dimension means "of the same value".

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  • That's a clear explanation! I wasn't actually thinking about sizes in multiple dimensions, but simply whether or not the plural has to / can be used just because there are multiple balls. So it seems it's more natural not to use the plural form but it's not incorrect to use it - and if you want to explicitly talk about multiple dimensions then you have to use it. – Andrew Sep 19 '15 at 22:21

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