E) If T is in second, we know M must then be in first, because of rule two (M before T). However, if M is then in first we know P must be in third, because of rule 4 (there must be exactly one performance between M and P). E goes south here because we now have P tied to spot 3. But we know from the last rule that P must perform first or seventh, so E is out.
D) If S performs 7th, then according to the last rule that means P performs first (since it can’t perform 7th if S does). If P performs first, then we know M must perform third because of the 4th rule again (there must be exactly one performance between M and P). From there, there are a couple possible combinations that work out. You could have P-L-M-O-N-T-S, or P-O-M-L-N-T-S.
