Combinatorics: What Are Graphs?

$$\text{Taking Sides}$$

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Six people are attending a party on a deserted island in an old mansion. They are in the ballroom which has a wall of floor to ceiling windows that look out over the water. It is a moonless and stormy night. With a clap of thunder, the lights cut out, and there is a commotion as everybody stumbles around. Suddenly with a flash of lightning, the entire room is illuminated, revealing who scurried to the right and left sides of the ballroom. It goes dark just as quickly, and the guests hear a gunshot. The lights flicker back on to reveal Mr. Adler has been shot. He is barely conscious, lying in the center of the room with a gun next to him.

"If we figure out who was on the left side of the room and who was on the right side, we can identify the shooter from the gunshot angle," says Mr. Elliott.

"In the flash of lightning, I saw Mr. Elliott on the opposite side of the room from me," says Ms. Burns.

"I saw Mrs. Freeman on the other side from me," says Mr. Collins.

"I clearly saw Ms. Burns' face on the other side from me," says Dr. Davis.

"Mrs. Freeman was on the opposite side from me," says Mr. Elliott.

"Ms. Burns was on the other side from me," says Mrs. Freeman.

"Ms. Burns and Mr. Collins were on opposite sides from each other," gasps Mr. Adler, as his last words.