Okay so the question tells us that spots 1 and 4 are P and spots 2 and 5 are Y. We know from rule #1 that any time Y and P are next to each other, any bead that immediately follows and any bead that immediately precedes that pair must be red. So that means spots 3 and 6 are going to be R.
Now rule #4 tells us that any portion of the strand containing eight consecutive beads must include at least one bead of each color. So far we have P, Y and R. Meaning we still need a G and an O for the first eight beads. Since the 6th bead is R, and we know from rule #4 that an O can't be immediately next to an R, we know that spot #8 MUST be an O. This way we can get one O in the first series of eight beads to satisfy rule #4. We also need one G, meaning that the only spot remaining in our first series of eight beads, spot #7, will be G. Spot #9 is open to any color bead except for R, because rule #3 states we can't have an O and an R next to immediately one another.
Thus, we cannot have "GGO" as the last three in the strand because the 8th must be an O. We can have "GOG" be the last three in the series, but that is not an answer choice given to us.
Hope that was helpful! Please let us know if you have any other questions.
alliehall21February 24, 2020
Why does G have to be 8? Why couldn't it be 9 and we configure the other letters differently in 7 and 8? For example, 7,8,9 being Y,G,O respectively or G,O,Y respectively (making B or E possible)
alliehall21February 24, 2020
Never mind I understand now.. it's because we have to fit all the colors inside the first 8 if I understand correctly.
SkylarMay 2, 2020
@alliehall21, yes, you seem to be understanding correctly now. Glad you figured it out. Please let us know if you have any other questions!
