As someone who lived in Pembrokeshire for some of his most formative years, and still has family connections there, I find it depressing that "Dyfed" needed to be allowed as an alternative answer to this question.
This is not to say I don't think it should have been; as the question didn't qualify what was meant by a county, I agree that it did need to be allowed.
As most readers of this website will know, Dyfed was one of the counties created by the Local Government Act of 1972, which took effect in 1974. Dyfed consisted of the traditional counties of Cardiganshire, Carmarthenshire and Pembrokeshire. The eight such counties in Wales were then abolished by the Local Government (Wales) Act 1994. Gwynedd and Powys still exist as two of Wales's 22 single–tier local government areas; but Dyfed does not (along with Clwyd and Gwent). The three parts of Glamorgan now make up eight of the 22 areas.
The eight former counties now exist only as the areas of jurisdiction of Sheriffs and Lord Lieutenants – known for convenience as "ceremonial counties". They are not counties in any meaningful sense. (The Sheriff is the Queen's legal representative in the relevant area; the Lord Lieutenant is her personal and military representative, responsible for organising the local militia.)
There is a lot of confusion these days about what is and is not a county. I even found a website entirely dedicated to the resolution of this issue: CountyWise.org.uk. This is brought to us by an organisation called the Association of British Counties: "a society dedicated to promoting awareness of the continuing importance of the 92 historic (or traditional) Counties of the United Kingdom."
Call me a stick–in–the–mud, but I am totally behind this cause. My family was living in Pembrokeshire when Dyfed was brought into existence, and I can state categorically that no one in Pembrokeshire took any notice. I doubt very much whether anyone in Cardiganshire or Carmarthenshire did either. I now live in Stockport, which is in the "ceremonial county" of Greater Manchester; but thank goodness the postal address is still Cheshire. The people of Stockport feel more akin to those in Macclesfield or Chester than those in Bolton, Bury, Oldham or Rochdale.
"Now", says CountyWise, "we live in an era of geographical confusion. The historic Counties are still important cultural entities. Many people have a strong sense of identity with them."
Hear, hear, says I!
Returning to the question of Wales's westernmost county: I would have been inclined to include the word "traditional" or "historic", thus ruling out Dyfed altogether. Anyone who answered "Dyfed" has surely, in any case, missed the point that Dyfed is no longer a real county, and hasn't been for twenty years now – if indeed it ever was.
© Macclesfield Quiz League 2018