Answer: It sounds as though your tomatoes had blossom end rot, a physiological condition caused by a lack of calcium at the blossom end of the fruit (the end opposite the stem). Even if your soil has adequate calcium, blossom end rot can occur if there are extreme fluctuations in soil moisture. The symptoms--blackening of flesh--take some time to develop, so the damage you see is actually the result of conditions some time back.
Remedies include having a soil test to make sure calcium levels are adequate, adding organic matter to a sandy soil to increase its moisture holding capacity, and keeping plants evenly moist, especially during the development of the first fruits. A thick layer of mulch helps maintain soil moisture.
Affected tomatoes are still edible. Just cut away the blackened portion.
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