This query returns count of unanswered questions of a certain user. The OtherUserID parameter is the ID of a user whose unanswered question count you want to get.
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DECLARE @OtherUserID INT = ##OtherUserID:int##
COUNT(*) AS [Unanswered Count]
OwnerUserId = @OtherUserID AND
PostTypeId = 1 AND
AcceptedAnswerId IS NULL