Interview stumper: friends of friends of friends

SELECT uid, friend_count
FROM user
WHERE uid IN (
    SELECT uid1
    FROM friend
    WHERE uid2 = me()
)

SELECT uid1
FROM friend
WHERE uid2 in (
    SELECT uid1
    FROM friend
    WHERE uid2 = me()
)

{
  "error": {
    "message": "Can't lookup all friends of 36807322. Can only lookup for the logged in user or the logged in user's friends that are users of your app.", 
    "type": "NoIndexFunctionException", 
    "code": 604
  }
}

SELECT f2.uid2 FROM friends f1
JOIN friends f2 ON f1.uid2 = f2.uid1
LEFT JOIN friends f3 ON f3.uid2 = f2.uid2 AND f3.uid1 = 'YourID'
WHERE f1.uid1='YourID' 
AND f2.uid2!='YourID'
AND f3.uid2 IS NULL

select e.*
from entities e
where e.entity_id <> :user_id and
      not exists (select 1
                  from friends f
                  where f.category <> 4 and
                        :user_id in (f.entity_id1, f.entity_id2) and
                        e.entity_id in (f.entity_id1, f.entity_id2)
                 ) and
      (select count(*)
       from friends f1 join
            friends f2
            on f1.entity_id1 = f2.entity_id1 or
               f1.entity_id1 = f2.entity_id2 or
               f1.entity_id2 = f2.entity_id1 or
               f1.entity_id1 = f2.entity_id2
       where :user_id in (f1.entity_id1, f1.entity_id2, f2.entity_id1, f2.entity_id2) and
             e.entity_id in (f1.entity_id1, f1.entity_id2, f2.entity_id1, f2.entity_id2)
      ) >= 2