The night before the Death Race across the Wastelands is set to begin, your uncle, the great inventor Slate Kanoli, got kidnapped by the ruthless No-Side gang. The only way to get him back is to race his Coil Runner against the gang yourself. Win and they’ll give back your uncle. Lose and you’ll forfeit the Coil Runner and all his other creations. As the grueling race gets underway, you find yourself falling further and further behind. Your only chance is to take a shortcut your uncle told you about–– the Flux Ravine gambit.
Fortunately, the Coil Runner comes equipped with emergency turbo thrusters. Unfortunately, your uncle was a notorious tinkerer, and the system still had some kinks to work out. Just minor things like the ignition exploding, the reactor leaking, or the oxygen levels depleting— any of which would end your racing career immediately. Before his kidnapping, Uncle Slate determined that each of these critical failures was the ultimate result of a chain reaction originating in the thrusters. He was also certain that while one factor could trigger two different effects, and two factors could each independently lead to the same effect, no effect is caused by two factors in conjunction. However, Uncle Slate never got around to pinpointing which thruster was responsible for which error. All you have are the notes from his test runs:
1. When thrusters B and C are on, the Fuel gauge glows.
2. When thrusters A, B, and D are on, the Fuel gauge glows and the Helium tank rattles.
3. When thrusters C, D, and E are on, the Fuel gauge glows and the Gravitometer spins.
4. When thrusters A, D, and E are on, the Gravitometer spins and the Helium tank rattles.
5. Shortly after the Helium tank rattles and the Gravitometer spins, the Ignition explodes and the Oxygen levels deplete.
6. Shortly after the Fuel gauge glows and the Gravitometer spins, the Reactor leaks.
You need to use as many thrusters as possible to give yourself the best chance at clearing the gap, without triggering any of the three catastrophic failures. Which thrusters should you activate?
Answer in 3 Answer in 2 Answer in 1
The most important thing to remember here is that even if we know that one thing causes another, the converse is not necessarily true. For example, this panic switch shuts off the coil runner’s engine. But the engine being off doesn’t necessarily mean the panic switch was engaged— the coil runner could be out of fuel, or damaged— or turned off normally. We can, however, conclude that if the engine is running, the panic switch hasn’t been engaged.
With that in mind, one way we can start is to work backwards from the three defects that could knock you out of the race. So let’s look at Slate’s last two notes, since they give direct information about those. The Gravitometer spins in both cases, but the results are different. That means the spinning Gravitometer can’t be the cause of any particular malfunction. If it were, the same thing would happen each time. So we can conclude that a glowing Fuel gauge makes the reactor leak, while a rattling Helium tank makes the Ignition explode and depletes the Oxygen levels.
Once we know which two errors we need to avoid, we can make a table and use the logic of cause and effect to see which thrusters trigger them. Since the Helium tank is fine during the first test run when thrusters B and C are active, we can assume neither makes it rattle. And from the third run we know that D and E don’t either. That leaves thruster A, which was indeed used in the second and fourth test runs where the Helium tank rattled.
Now what causes the glowing Fuel gauge? From the fourth test run we know it can’t be thrusters A, D, or E. So is the culprit, B, C, or each of them separately? The answer can be found in the second and third test runs: the fuel tank glowed in both, but B was activated in one, and C in the other. That means the B and C thrusters each independently make the Fuel tank glow.
It looks like the A, B, and C thrusters are off limits. Fortunately, the other two are just enough to clear the jump. You rocket into first place and the gang begrudgingly hands over your uncle. He thanks you profusely, and decides to celebrate your victory with a cup of tea from his latest contraption...
