So here's what we start with. As an example of the terminology, cell e3 contains an A, and cell d3 is part of region R.
Region Y needs a string with a Y two from the end. Strings 4 and 5 are the only strings that will fit. But using string 5 would put an O in b2, and column b already has an O. So string 4 belongs in region Y.
Region G has a G at one end, and strings 1 and 3 are the only ones left that can provide that. But string 1 won't fit at all. Its A would go in e7, which conflicts with e3; its P in d7 conflicts with d6; its B in c7 with a7; and its O in b7 with b4. So string 3 belongs in region G.
Region R needs a string with an O at one end, and there are three left (strings 2, 5, and 7). Column 2 needs a Y and an R, and since row 5 already has a Y, b5 must be R. String 2 is the only one with an O-R on the end, so it belongs it region R.
String 1 is the only one left that can fit region B. Either string 6 or 7 might fit region P, but string 7 would put B in c6, while row 6 already has a B. So string 6 belongs in region P.
The remaining two strings can only fit the two empty regions in one way; string 5 goes in region R and string 7 goes in region A.
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