Get the $100 bill (mathematician, a physicist, and an engineer) following a simple rule:
When they have walked half the distance to the wall, they have to stop and wait for a second.
A researcher pins a $100 bill on the wall, and tells a mathematician, a physicist, and an engineer that they can have the money if they can cross the room to get it. They just have to follow this one rule. When they have walked half the distance to the wall, they have to stop and wait for a second.
The mathematician thinks about this and walks away.
The physicist walks halfway across the room, waits a second, then walks half the remaining distance and thinks about it, and walks away.
The engineer walks halfway across the room, waits a second, walks half the remaining distance and waits a second, walks half the remaining distance and waits a second, walks half the remaining distance and waits a second, walks half the remaining distance and waits a second, then walks half the remaining distance and thinks, "That's close enough!" grabs the $100 bill and walks away.