The schedule of the paintings shown in the four weeks is completely determined if which one of the following is true?

Emil-Kunkin on April 25 at 06:58PM

I suggest testing out the variables with the most restrictions first.

While it is good to test out the variables with the most restrictions first (as they are most likely to be able to fully determine the order), that does not automatically mean they will be right.

Lets try to see what happens if H is shown twice. We know that in order to show H twice, I must be in week 1, and since H cannot be two weeks in a row, H must be 2 and 4, so G must be 3

I H G H
_ _ _ _

However, we cannot determine which of the watercolors go where. We know that At least one S must be with one of our Hs, and that G and P can't be together, but we could have several possible arrangements.

H has many restrictions, but I think that S is actually more restricted than H since S can only appear when H appears. That is if S appears twice, then H must also appear twice. Since we know the order of the top row if H appears twice, and that S will be with both of the Hs, we could diagram this as

I H G H
_ S _ S

And since G cannot be with P we know that P is first, that R is third, so this is fully determined.

I H G H
P S R S