You are the commander of a spaceship that is running low on fuel. You have three fuel tanks, each with a different capacity: Tank A can hold 1000 L, Tank B can hold 2000 L, and Tank C can hold 3000 L. The fuel gauges are broken, and you only know that one tank is full, one tank is half‑full, and one tank is empty. You can send exactly one message to Mission Control. Which single piece of information should you send to guarantee you can determine the status of every tank?
Correct: Send the difference in fuel levels between Tank A and Tank B
Sending the difference between the fuel in Tank A and Tank B is enough to pin down the whole situation. There are only three possible assignments of "full", "half‑full" and "empty" to the three tanks, because each capacity is distinct:
1. A = full (1000 L), B = half (1000 L), C = empty (0 L) → difference A‑B = 0 L
2. A = full (1000 L), B = empty (0 L), C = half (1500 L) → difference A‑B = 1000 L
3. A = half (500 L), B = full (2000 L), C = empty (0 L) → difference A‑B = -1500 L
4. A = half (500 L), B = empty (0 L), C = full (3000 L) → difference A‑B = 500 L
5. A = empty (0 L), B = full (2000 L), C = half (1500 L) → difference A‑B = -2000 L
6. A = empty (0 L), B = half (1000 L), C = full (3000 L) → difference A‑B = -1000 L
Each possible difference value (0, 1000, ‑1500, 500, ‑2000, ‑1000) occurs only once among the six arrangements, so Mission Control can look at the reported difference and instantly know which tank is full, half‑full, and empty. The other three answer choices do not give a unique mapping: the total fuel could correspond to several arrangements, the amount in Tank A alone leaves ambiguity, and knowing the level of the largest tank (C) still leaves two possibilities for A and B. Hence the correct choice is the third one.