Detroit Tigers First-Place Eliminiation Scenario
Detroit must win 27 more games (27 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Detroit finishes in first place with 27 wins:

Team             W	L	PCT	GB
Detroit          27	135	0.167	0.00
Kansas City      27	135	0.167	0.00
Cleveland        27	135	0.167	0.00
Chicago          26	136	0.160	1.00
Minnesota        26	136	0.160	1.00

Tie breakers
Detroit wins the series with Cleveland 7 games to 6
Detroit wins the series with Kansas City 7 games to 6

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          0	0	162	0.000	0.0
Cleveland        0	0	162	0.000	0.0
Detroit          0	0	162	0.000	0.0
Kansas City      0	0	162	0.000	0.0
Minnesota        0	0	162	0.000	0.0

Next, we show how the remaining series of games plays out in the scenario:

Chicago currently has 0 win(s) against Cleveland and 0 loss(es).
Chicago wins 4 additional game(s) against Cleveland and loses 9.
Chicago loses the series 4 games to 9.
Chicago wins 0 additional game(s) against teams outside the division and loses 110.

Chicago currently has 0 win(s) against Detroit and 0 loss(es).
Chicago wins 8 additional game(s) against Detroit and loses 5.
Chicago wins the series 8 games to 5.
Chicago wins 0 additional game(s) against teams outside the division and loses 110.

Chicago currently has 0 win(s) against Kansas City and 0 loss(es).
Chicago wins 1 additional game(s) against Kansas City and loses 12.
Chicago loses the series 1 games to 12.
Chicago wins 0 additional game(s) against teams outside the division and loses 110.

Chicago currently has 0 win(s) against Minnesota and 0 loss(es).
Chicago wins 13 additional game(s) against Minnesota and loses 0.
Chicago wins the series 13 games to 0.
Chicago wins 0 additional game(s) against teams outside the division and loses 110.

Cleveland currently has 0 win(s) against Detroit and 0 loss(es).
Cleveland wins 6 additional game(s) against Detroit and loses 7.
Cleveland loses the series 6 games to 7.
Cleveland wins 1 additional game(s) against teams outside the division and loses 109.

Cleveland currently has 0 win(s) against Kansas City and 0 loss(es).
Cleveland wins 6 additional game(s) against Kansas City and loses 7.
Cleveland loses the series 6 games to 7.
Cleveland wins 1 additional game(s) against teams outside the division and loses 109.

Cleveland currently has 0 win(s) against Minnesota and 0 loss(es).
Cleveland wins 5 additional game(s) against Minnesota and loses 8.
Cleveland loses the series 5 games to 8.
Cleveland wins 1 additional game(s) against teams outside the division and loses 109.

Detroit currently has 0 win(s) against Kansas City and 0 loss(es).
Detroit wins 7 additional game(s) against Kansas City and loses 6.
Detroit wins the series 7 games to 6.
Detroit wins 1 additional game(s) against teams outside the division and loses 109.

Detroit currently has 0 win(s) against Minnesota and 0 loss(es).
Detroit wins 7 additional game(s) against Minnesota and loses 6.
Detroit wins the series 7 games to 6.
Detroit wins 1 additional game(s) against teams outside the division and loses 109.

Kansas City currently has 0 win(s) against Minnesota and 0 loss(es).
Kansas City wins 1 additional game(s) against Minnesota and loses 12.
Kansas City loses the series 1 games to 12.
Kansas City wins 1 additional game(s) against teams outside the division and loses 109.

# Detroit Tigers' magic number
# Detroit's magic number
# Tigers' magic number
# MLB Playoff Race