Olive Picking (Outliers of Hyperborea Part VI)

Olives are an important staple in Hyperborea, and olive picking is an occupation engaged in by many inhabitants. Four olive pickers are having a discussion. One is known to be a Sororean, one is known to be a Nororean, one is known to be a Midrorean, and one is known to be an Outlier. Their statements follow:

1. 1. I picked more olives today than anyone else.
   2. I am the Midrorean.
   3. C is the Outlier.
2. 1. I am the Midrorean.
   2. I would have picked more olives today than A, except that I did not start until after lunch.
   3. C is the Outlier.
3. 1. D dropped more olives than he picked.
   2. I picked more olives today than A did.
   3. B picked olives all day today.
4. 1. C picked more olives today than A did.
   2. I did not drop any olives today.
   3. B would have picked more olives than A today, except that he did not start until after lunch.

Which one is the Sororean, which one is the Nororean, which one is the Midrorean, and which one is the Outlier?

The key to getting started on this one is to note that neither A nor B can be the Sororean because they each claimed to be something else. This leaves C and D. If C is the Sororean then A's first statement, at least, is false. The possibility that A might be a Midrorean with order FTF is tempting and we will run with it. This leaves either B or D to be the Outlier.

If B is the Outlier then his first statement is false and so is his third statement. This constrains his second statement to being true. If B is the Outlier then all that is left for D to be is the Nororean. However, the falsity of D3 is not compatible with the putative truth of B2, because the statement negated in one instance and accepted as true in the other is essentially the same. This means B is not the Outlier.

If D is the Outlier than his first and second statements are true and false, respectively. The truth value of the third can be determined by recognizing that it is now B who is constrained to be the Nororean. Because this entails that B2 is false, then so is D3. Additionally, B1 and B3 also check out as false statements, confirming this impression.

Final answer: A is the Midrorean, B is the Nororean, C is the Sororean and D is the Outlier.