To find the number of cotton candy pumpkins that Rory has, we first need to calculate the total number of lumina, jack o'little, and sugar pie pumpkins that he has. Since 1/4 of the pumpkins are lumina pumpkins, this means that Rory has 1/4 * 180 = 45 lumina pumpkins. Since 1/6 of the pumpkins are jack o'little pumpkins, this means that Rory has 1/6 * 180 = 30 jack o'little pumpkins. And since 1/10 of the pumpkins are sugar pie pumpkins, this means that Rory has 1/10 * 180 = 18 sugar pie pumpkins.
Next, we need to add up the number of lumina, jack o'little, and sugar pie pumpkins to find the total number of pumpkins that are not cotton candy pumpkins. This gives us a total of 45 + 30 + 18 = 93 pumpkins that are not cotton candy pumpkins.
Finally, we need to subtract the number of non-cotton candy pumpkins from the total number of pumpkins that Rory has to find the number of cotton candy pumpkins. This gives us 180 - 93 = <<180-93=87>>87 cotton candy pumpkins. Therefore, Rory has 87 cotton candy pumpkins