On a voyage to atlantis, ariel from the little mermaid decided to pick up shells so that she could make necklaces for her mermaid friends. she picked up 30 green shells, 35 blue shells, and 30 yellow shells. 17 of the green shells had some blue in them. 15 of the shells had both yellow and blue in them, and 10 of the shells had both yellow and green in them. if just one shell had all three colors in it, how many total shells did ariel pick up?

54. You have to go from the more colour they have. You have 1 all three coloured, you have 17 which has both blue and green, but the all three coloured has both colours in it too, so it's one plus sixteen. You go around with this logic with the more coloured ones, then you have the one coloured groups. You have 30 green but you had the all three coloured, and two kinds of two coloured (1+9+16+x=30). You go around with this logic on this group, then count (6+4+4+9+16+14+1=54)