If you want to search for entities which contain a "Foo" part then you need to do:

SELECT entity_id
FROM entities
WHERE part1='Foo'
OR part2='Foo'
OR part3='Foo'
...
OR part12='Foo';
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Or perhaps slightly more concise:

SELECT entity_id
FROM entities
WHERE 'Foo' IN (part1, part2, part3, ..., part12);
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I'd much prefer something like:

SELECT e.entity_id
FROM entities e
INNER JOIN entity_parts ep ON e.entity_id=ep.entity_id
WHERE ep.part='Foo'
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When you get to searching for different combinations of parts, the advantages of joining become even more apparent:

SELECT e.entity_id
FROM entities e
INNER JOIN entity_parts ep1 ON e.entity_id=ep1.entity_id
INNER JOIN entity_parts ep2 ON e.entity_id=ep2.entity_id
WHERE ep1.part='Foo'
AND ep2.part IN ('Bar', 'Baz')
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And in terms of the e-mail example, it's much easier to, say, enforce a UNIQUE constraint over a single column.