In British English:
(1) Tom and Peter played the guitar.
a. There was one musical instrument that T and P played on some past occasion (s), not simultaneously.
b. T and P had the musical ability but, as Ted suggested, they did not actually perform.
(2) Tom and Peter played the guitars.
There were two guitars and T and P played one each on some occasion(s) in the past.
(3) Tom and Peter played guitars.
There is no suggestion as to how many guitars were available. T and P played one each on some occasion(s) in the past
I also see "Old Scottish saying" in the internet, is that correct?
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