First find how many purple horses there are: 3 blue horses * 3 purple/1 blue = <<3*3=9>>9 purple horses

Then double that number to find how many green horses there are: 9 purple horses * 2 green/1 purple = <<9*2=18>>18 green horses

Then divide the number of green horses by 6 to find the number of gold horses: 18 green horses / 6 green/1 gold = <<18/6=3>>3 gold horses

Then add the number of horses of each color to find the total number of horses: 9 horses + 18 horses + 3 horses + 3 horses = <<9+18+3+3=33>>33 horses

# Answer

33
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The carousel at the fair has 3 blue horses, three times that many purple horses, twice as many green horses as purple horses, and 1/6th as many gold horses as green horses. How many horses are there total?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
33
The carousel at the fair has 3 blue horses, three times that many purple horses, twice as many green horses as purple horses, and 1/6th as many gold horses as green horses. How many horses are there total?
train