Solution: Radio Broadcast
Answer: PARABOLIC
Written by Josh Alman and Ian Osborn
This puzzle consists of an audio file of the end of a baseball game. The batters for each team are in order alphabetically by last name, which suggests that their order does not matter. However, for most of the defensive plays, the fielders are referred to either by position or by name, but not both. This suggests that the solver will need to identify which player is playing at each position. (For full details about how to do so, see below.) The commentators also mention fielding position numbers, which give a method for extracting letters from the players’ last names.Away Team
| Position Number | Position | Player | Extracted Letter |
|---|---|---|---|
| 1 | Pitcher | Duke Snider | S |
| 2 | Catcher | Billy Butler | U |
| 3 | First Base | Bruce Campbell | M |
| 4 | Second Base | Edgar Martínez | T |
| 5 | Third Base | Red Faber | R |
| 6 | Shortstop | Kole Calhoun | U |
| 7 | Left Field | Carl Yastrzemski | E |
| 8 | Center Field | Burke Badenhop | P |
| 9 | Right Field | Martín Maldonado | O |
Home Team
| Position Number | Position | Player | Extracted Letter |
|---|---|---|---|
| 1 | Pitcher | Tris Speaker | S |
| 2 | Catcher | Warren Spahn | P |
| 3 | First Base | Enos Slaughter | A |
| 4 | Second Base | Joe McGinnity | I |
| 5 | Third Base | Phil Niekro | R |
| 6 | Shortstop | Kurt Stillwell | W |
| 7 | Left Field | Evan Longoria | I |
| 8 | Center Field | Bernie Williams | S |
| 9 | Right Field | Brett Saberhagen | E |
| Position (in game) | Away Team Player | Real Position Number | Home Team Player | Real Position Number | Sum of Position Numbers | Letter |
|---|---|---|---|---|---|---|
| Pitcher | Duke Snider | 8 | Tris Speaker | 8 | 16 | P |
| Catcher | Billy Butler | 0 | Warren Spahn | 1 | 1 | A |
| First Base | Bruce Campbell | 9 | Enos Slaughter | 9 | 18 | R |
| Second Base | Edgar Martínez | 0 | Joe McGinnity | 1 | 1 | A |
| Third Base | Red Faber | 1 | Phil Niekro | 1 | 2 | B |
| Shortstop | Kole Calhoun | 9 | Kurt Stillwell | 6 | 15 | O |
| Left Field | Carl Yastrzemski | 7 | Evan Longoria | 5 | 12 | L |
| Center Field | Burke Badenhop | 1 | Bernie Williams | 8 | 9 | I |
| Right Field | Martín Maldonado | 2 | Brett Saberhagen | 1 | 3 | C |
Determining Which Player Plays at Each Position:
(Bot 7) On Joe McGinnity’s ground ball out, Kole Calhoun fielded the ball and took it to second base himself, which means he is either the second baseman or the shortstop for the away team.
(Bot 7) On Brett Saberhagen’s single, we are told that the away team’s center fielder is normally a pitcher. Once we hear the names of all of the away team players, we can narrow down their center fielder to either Red Faber or Burke Badenhop.
(Bot 7) During Enos Slaughter’s at bat, we are told that Red Faber is closer to the third base dugout than Edgar Martínez. We will use this information later.
(Bot 7) Also during Enos Slaughter’s at bat, we are told that the away team’s catcher is normally a designated hitter. Again, once we hear the names of all of the away team players, we can narrow down their catcher to either Billy Butler or Edgar Martínez.
(Top 8) On Burke Badenhop’s ground ball, we are told that the ground ball goes past Enos Slaughter and into the outfield, meaning that Slaughter is the home team’s pitcher, first baseman, second baseman, third baseman, or shortstop.
(Top 8) On Billy Butler’s double, we are told that the ball was hit along one of the two foul lines, and Evan Longoria fielded it and threw it back in to the infield. Therefore, Longoria is the home team’s left fielder or right fielder.
(Top 8) During Kole Calhoun’s at bat, we are told that Burke Badenhop and Phil Niekro are standing at the same base. Since Badenhop is the runner at third base after Butler’s double, this means that Phil Niekro is the home team’s third baseman.
(Top 8) Also during Kole Calhoun’s at bat, we are told that only two of the home team’s players are at their natural positions. We will use this information later.
(Top 8) On Bruce Campbell’s fly ball out, we are told that the home team’s right fielder, first baseman, and catcher all have last names beginning with the letter S. Therefore, Longoria cannot be their right fielder, so Evan Longoria is the home team’s left fielder.
(Bot 8) The home team’s catcher leads off the bottom of the 8th inning. Warren Spahn was at bat in the bottom of the 7th when the hidden ball trick ended the inning, so he also bats to lead off the bottom of the 8th. So, Warren Spahn is the home team’s catcher.
(Bot 8) The home team’s catcher (Warren Spahn) hits a pop-up near the right fielder and first baseman, and Bruce Campbell catches it, so he plays one of these two positions for the away team.
(Bot 8) On Tris Speaker’s fly ball out, we are told that Carl Yastrzemski is the away team’s left fielder.
(Bot 8) During Kurt Stillwell’s at bat, we are told that the defense employs the shift. Stillwell hits a ground ball to the right side of the infield, where Edgar Martínez fields it and throws to the first baseman. This implies that Martínez is the away team’s second baseman or third baseman. Therefore, since he cannot be the catcher, the away team’s catcher must be Billy Butler. Also, since Red Faber is closer to the third base dugout than Martínez, Martínez cannot be the third baseman (the position closest to the third base dugout), so Edgar Martínez is the away team’s second baseman. Therefore, Calhoun cannot be their second baseman, so Kole Calhoun is the away team’s shortstop.
(Top 9) After Martín Maldonado’s single, we are told that both teams’ pitchers are normally center fielders. Once we hear the names of all of the players, we can identify that the away team’s pitcher is Duke Snider, and that the home team’s pitcher is either Tris Speaker or Bernie Williams.
(Top 9) On Duke Snider’s pop-up, we are told that Joe McGinnity makes the catch, so he is the home team’s first baseman, second baseman, third baseman, or shortstop. We can eliminate third base as a possibility since we already know that Phil Niekro is the home team’s third baseman. We can also eliminate first base as a possibility, since the home team’s first baseman’s last name starts with the letter S. So McGinnity is the home team’s second baseman or shortstop.
(Bot 9) On Bernie Williams’s home run, Martín Maldonado tries to make the catch, so he is an outfielder for the away team. Since Yastrzemski is their left fielder and their center fielder is either Faber or Badenhop, Martín Maldonado is the away team’s right fielder. Since Campbell can no longer be the right fielder, Bruce Campbell is the away team’s first baseman. At this point, there are only two positions (third base, center field) and two players (Red Faber, Burke Badenhop) remaining for the away team. Since Red Faber is closer to the third base dugout than Edgar Martínez, the second baseman, Red Faber is the away team’s third baseman. This leaves Burke Badenhop as the away team’s center fielder.
(Bot 9) After Bernie Williams’s home run, we are told that Williams and Slaughter do not both play infield positions. Since we know from earlier that Slaughter is an infielder, Bernie Williams must be an outfielder for the home team. Since Longoria is the home team’s left fielder and their right fielder’s last name starts with the letter S, Bernie Williams is the home team’s center fielder. This also leaves Tris Speaker as the home team’s pitcher.
We are now left with four players (Enos Slaughter, Joe McGinnity, Kurt Stillwell, Brett Saberhagen) and four positions (first base, second base, shortstop, right field) for the home team. Since Bernie Williams is the only home team player at his natural position so far, exactly one of the four remaining players plays at their normal position. There are two possibilities: Enos Slaughter at right field or Kurt Stillwell at shortstop. However, we know from earlier that Slaughter is an infielder, so Kurt Stillwell must be the home team’s shortstop. Therefore, Joe McGinnity can only be the home team’s second baseman. Since Slaughter is an infielder, Enos Slaughter is the home team’s first baseman. Finally, this leaves Brett Saberhagen as the home team’s right fielder.
Author’s Notes
We had been discussing making a puzzle in the form of a baseball radio broadcast for a long time, and we're very happy with how this one turned out! We tried to make the puzzle accessible to people who don't know a lot about baseball, for instance by explaining position numbers and the infield shift as part of the broadcast, and carefully wording what we said to avoid ambiguities for someone unfamiliar with baseball lingo. At the same time, we included a few fun things that baseball fans would enjoy, and non-baseball fans might look up and appreciate, like the hidden ball trick and a nod to the home run ball which bounced off of Canseco's head. We aimed to use recognizable player names when our final extraction mechanism allowed it, and most of the players in our game are either current players or Hall of Famers.