jeastman Wrote:I have a question. Because X has more records than any other place, I put a dash on one line for everyone else ( S,T,V, and Z.) Now, because J can only be pin S and X, does that mean I add another line to V and Z?
As Noah said, that is right. That is one less slot that V and Z can have.
This is how my diagram looked, although I chose to have lines or slots that indicate that some variable must be placed there rather than the box.
I chose to have the base of my setup be the stores, as I know that each store must have at least 1 of the 4 music types. As of now, I do not even know that every music type will be used.
So I will be assigning FJOR into STVXZ.
My first rule tells me that I will have exactly 2 J's placed. I indicate this on my diagram to keep track of it.
I am then told that T has R and O, and that those are the only ones it carries. I can now wall off this store, as it cannot contain any more music types.
S carries more than T. We know that T carries exactly 2. This means that S must carry at least 3. I will indicate such with 3 lines. It could carry all 4 at this moment, but it is not something that must be true. This is why I will not place the fourth line there. But I will not also wall it off after the 3rd slot.
My next rule is that X carries more types of music than any other store. Since I know that S carries at least 3, I know that X must carry all 4 in order for it to have more than any other store.
This also means that S is walled off at 3. It cannot have 4 because at that point X would be tied with a store, and this rule says more than any other store.
With X having four lines, that means it has all four types FJOR. This means that one of our 2 J's is used. I now erase one of the J's. I have one J left to place. As of now, the J must go into either S, V, or Z.
My next rule tells me that S carries J. So now I have no J's left to distribute. I can write ~J beside V and Z. I now only have 2 types left to place in S. It must be 2 of F, O, and R.
My next rule states that V and Z have none in common. So I know that with only 3 variables left in play: FOR....that the maximum amount either V or Z could have is 2. For one of those stores to contain three items is possible. As this would necessarily cause sharing between V and Z.
With this global set up, I see that the issue is going to be the V-Z distinction. S simply has to choose 2 of FOR, and its basis of selection has no impact on the V-Z distinction.