Approach to removing dandelions?

Without chemicals, our lawn has sprouted a great patch of dandelions. I know that I could use products like corn gluten meal to diminish them, but I am curious about another idea. Would it be possible to eradicate dandelions if I consistently picked them, removing the heads before they could turn to seed? Or, is would that be a fruitless effort? Thanks!

Answers:
I disagree with the people that say don't worry about picking them... besides the fact that it is good exercise ... if you do it right...you can get rid of the majority of your problem... you have to get down and get the tap root of the dandelion so wait till after it rains when the soil is loose and moist... then get a small shovel and attempt to uproot it all... if you don't get all of the root be persistant and it will eventually die out...there is only so much energy the roots can provide to make a new plant everytime its damaged... use the leaves in salads or make wine with the flowers... i have also heard that the milky sap is good for getting rid of warts... but it takes a month or 2... and the roots are a good coffee substitute when dried and ground...

Other answers:
it would be a fruitless effort because they will still be coming back.
it would be a fruitless effort because they will still be coming back.
Merely picking the dandelions would be a waste of time. They have deep roots and would grow back within days.

My understanding is that if your lawn is healthy, and you let your grass grow a little longer than usual, it'll squeeze out any weed that tries to set up shop.
Don't bother picking them! You could always buy a goat.
Waste of time, too many sources of seed.
get down on hands and knees and dig them up, get the root that way.
Forget the "without chemicals." Get roundup and a little dab will do ya...good by dandelions.
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