Washington Nationals First-Place Eliminiation Scenario
Washington must win 26 more games (36 total) to avoid elimination from first place.
Here are the final standings in a scenario in which Washington finishes in first place with 36 wins:

Team             W	L	PCT	GB
Washington       36	126	0.222	0.00
Philadelphia     36	126	0.222	0.00
New York         36	126	0.222	0.00
Atlanta          36	126	0.222	0.00
Miami            35	127	0.216	1.00

Tie breakers
Washington wins the series with Atlanta 7 games to 6
Washington wins the series with New York 7 games to 6
Washington wins the series with Philadelphia 7 games to 6

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Atlanta          17	6	139	0.739	0.0
Philadelphia     15	10	137	0.600	3.0
New York         13	11	138	0.542	4.5
Washington       10	13	139	0.435	7.0
Miami            6	20	136	0.231	12.5

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

Atlanta currently has 5 win(s) against Miami and 1 loss(es).
Atlanta wins 6 additional game(s) against Miami and loses 1.
Atlanta wins the series 11 games to 2.
Atlanta wins 0 additional game(s) against teams outside the division and loses 99.

Atlanta currently has 1 win(s) against New York and 2 loss(es).
Atlanta wins 3 additional game(s) against New York and loses 7.
Atlanta loses the series 4 games to 9.
Atlanta wins 0 additional game(s) against teams outside the division and loses 99.

Atlanta currently has 2 win(s) against Philadelphia and 1 loss(es).
Atlanta wins 4 additional game(s) against Philadelphia and loses 6.
Atlanta loses the series 6 games to 7.
Atlanta wins 0 additional game(s) against teams outside the division and loses 99.

Atlanta currently has 0 win(s) against Washington and 0 loss(es).
Atlanta wins 6 additional game(s) against Washington and loses 7.
Atlanta loses the series 6 games to 7.
Atlanta wins 0 additional game(s) against teams outside the division and loses 99.

Miami currently has 0 win(s) against New York and 0 loss(es).
Miami wins 7 additional game(s) against New York and loses 6.
Miami wins the series 7 games to 6.
Miami wins 0 additional game(s) against teams outside the division and loses 90.

Miami currently has 0 win(s) against Philadelphia and 0 loss(es).
Miami wins 13 additional game(s) against Philadelphia and loses 0.
Miami wins the series 13 games to 0.
Miami wins 0 additional game(s) against teams outside the division and loses 90.

Miami currently has 0 win(s) against Washington and 0 loss(es).
Miami wins 8 additional game(s) against Washington and loses 5.
Miami wins the series 8 games to 5.
Miami wins 0 additional game(s) against teams outside the division and loses 90.

New York currently has 0 win(s) against Philadelphia and 0 loss(es).
New York wins 3 additional game(s) against Philadelphia and loses 10.
New York loses the series 3 games to 10.
New York wins 1 additional game(s) against teams outside the division and loses 88.

New York currently has 0 win(s) against Washington and 0 loss(es).
New York wins 6 additional game(s) against Washington and loses 7.
New York loses the series 6 games to 7.
New York wins 1 additional game(s) against teams outside the division and loses 88.

Philadelphia currently has 2 win(s) against Washington and 1 loss(es).
Philadelphia wins 4 additional game(s) against Washington and loses 6.
Philadelphia loses the series 6 games to 7.
Philadelphia wins 1 additional game(s) against teams outside the division and loses 90.

# Washington Nationals' magic number
# Washington's magic number
# Nationals' magic number
# MLB Playoff Race