Mary not knowing obviously rules out row 3
Mary knowing that Jane doesn't know tells us that there for every column that has a blue square in the correct row there must be at least one other blue square in that column. This rules out row 4, as if it was in C4 then Jane would know so Mary couldn't say with certainty that Jane doesn't know.
Having ruled out rows 3 and 4, the only way that Jane can now know where the prize is is if there is exactly one blue square in rows 1 and 2 of the correct column. This is only the case for column A, so the prize must be in A2.

I see Row 3 and Column C easily ruled out.

But in Row 4 what is it that allows them to exclude either 4A or 4D as BOTH being LIVE potential hosts and thus keeping that Row in play?

Consider what happens if Mary was told Row 4. She would know that one of 4A, 4C or 4D was correct. However since 4C is a possibility then as far as Mary knows Jane could have been told column C, in which case Jane would know, so this means that if Mary was told row 4 then she would not be able to make the statement about Jane not knowing.

Given what Mary says:

- Yes Jane clearly can say it is not at C4 based on what Mary would instantly know if it was...
- But in Janes view neither A4 nor D4 can be excluded (??) by Mary as potential hosts ...or can they? If so, how?

I'm not sure if I'll be able to make it much clearer but I'll give it another go.

Assume Mary was told the prize was in row 4. Mary doesn't know exactly where the prize is but knows it must be in A4, C4 or D4. If the prize was in A4 or D4 then Jane also wouldn't know where the prize is, however if the prize was in C4 then Jane would know the prize is. This means that Mary does not know whether or not Jane knows where the prize is and therefore would not be able to make the statement that Jane also does not know where the prize is. Since Mary did make that statement (and we are told the statements are correct) then this contradicts our initial assumption so Mary must not have been told row 4.

By using this logic (and the more straightforward fact that it can't be row 3 or Mary would have known the location) Jane can rule out Mary having been told that the prize is in row 3 or 4. Having done this it's hopefully obvious that Jane must have been told column A because otherwise she would still not know where the prize is (it could be either row 3 or 4 if she had been told column B or D).

This is essentially the same puzzle but it was interesting to me that it still works with the knowledge reversed but results in a different answer.

Funny enough I initially had meant to say numbered row and lettered column in the OP so it was obvious even if you didn't know the convention. But I liked the fact that it still happened to work so I left the mistake since someone using the opposite convention could still correctly explain their answer.