According to baseball rule...
10.19(f) No pitcher shall be credited with pitching a shutout unless he pitches the complete game, or unless he enters the game with none out before the opposing team has scored in the first inning, puts out the side without a run scoring and pitches all the rest of the game.
When two or more pitchers combine to pitch a shutout a notation to that effect should be included in the league's official pitching records.
So according to the bolder part a relief pitcher can come in the first inning with two or three runners on. The first batter he faces hits into a triple play. He then procedes to retire the side in order the next 8 innings so the correct answer would be 25
On May 31, 1988, Neil Allen faced more than 25 batters but he was credited with a shutout despite not starting the game. http://www.baseball-reference.com/boxes ... 5310.shtml