Answer: Lettuce, peas and radishes are all early crops and prefer cool weather. They could be replaced once they fade with cucumbers and melons because they need warm weather to thrive. Melons however take a very long season to mature, so keep that in mind when you make your selection and look for a fast grower. You might want to grow a bush type of cucumber to save space, or try trellising the melons and cucumbers to conserve space. Otherwise, be prepared to let them scramble. Strawberries are problematic in that they will not winter over well in the boxes. You might try an everbearer or the tiny European type so you can enjoy berries all summer. Carrots in particular do well in containers where you can make sure the soil is well prepared and slightly sandy; you may want to grow these alone due to their special soil needs. You might also add a few herbs such as chives, parsley and basil since it will be on your patio.
While you are planning, you might want to take a look at a book or two about container gardening. One I like is "Container Gardening for Dummies" by Bill Marken, ISBN 0-7645-5057-8. In it you will find discussions about soil for containers as well as watering and selecting what to grow.
In terms of patterns, The boxes are small and will be crowded. Often you can use, smaller or earlier maturing plants around a larger one, such as herbs around a tomato, but the arrangement is dictated more by cultural needs than looks. If they are healthy, they will look nice enough.
Good luck with your experiment!
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