Beans and other edibles are pretty quick. If you make a sprouter you can go from seeds to eating sprouts in less than a week.
http://forums.armageddononline.org/threads/32203-Sprouts-could-double-your-food-preps Avoid pinto beans. My favorite sprouts are mung beans, garbonzo beans, lentils and black eyed peas. Pinto beans are junk compared to these
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Cucumbers also grow very fast. They sprouted in a day, and are continuing to grow. They can be vine-like too, if it was for about a month he could most likely have them grow up yardsticks.
I hear lentils are pretty quick too, but everyone seems to agree on radishes.
Beans, peas, carrots, carrots. Almost any of the edible plants that can be eaten that aren't tree or bush harvested (apples, oranges, etc). They all germinate quickly. Flowers can take a bit longer to start. But definately beans, they get going very quickly. Also tyep's radishes - that is very quick.
My sons radishes sprouted in 1 day and now its day 2 and they have doubled.