First find the number of seeds that land in water: 300 seeds * 1/3 = <<300*1/3=100>>100 seeds

Then find the number of seeds that are eaten: 300 seeds * 1/6 = <<300*1/6=50>>50 seeds

Subtract the number of seeds that are destroyed to find the number that sprout: 300 seeds - 100 seeds - 50 seeds = <<300-100-50=150>>150 seeds

Then divide that number by 2 to find the number of sprouts that survive: 150 seeds / 2 = <<150/2=75>>75 seeds

# Answer

75
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Each dandelion produces 300 seeds. 1/3rd of the seeds land in water and die. 1/6 of the starting number are eaten by insects. Half the remainder sprout and are immediately eaten. How many dandelions survive long enough to flower?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
75
Each dandelion produces 300 seeds. 1/3rd of the seeds land in water and die. 1/6 of the starting number are eaten by insects. Half the remainder sprout and are immediately eaten. How many dandelions survive long enough to flower?
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