Question

After executing a sequence of instructions, bottle A contains one litre of water. The first and the third of these instructions are shown below: FILL (C, A)
______________________________
FILL (C, A) Then which of the following statements about the second instruction is true?

• A. The second instruction is FILL (B, A).
• B. The second instruction is EMPTY (C, B).
• C. The second instruction transfers water from B to C.
• D. The second instruction involves using the water in bottle A.
• A. 1
• B. 2
• C. 0
• D. None of the above

Answer 1

The Correct Option is B

Initial state: A = 5 L, B = 0 L, C = 0 L. Step 1: FILL (C, A) $\Rightarrow$ transfer from A to C until C full (capacity 2 L). A = 3 L, B = 0 L, C = 2 L. Step 2: To end up with A = 1 L after Step 3 (another FILL (C, A)), we must first empty C into B so that C becomes empty before Step 3. This is done by EMPTY (C, B) (capacity of B = 3 L). A = 3 L, B = 2 L, C = 0 L. Step 3: FILL (C, A) $\Rightarrow$ from A to C: transfer 2 L to fill C. A = 1 L, B = 2 L, C = 2 L. Condition satisfied: A has 1 L after Step 3. \[ \boxed{\text{Second instruction = EMPTY (C, B)}} \]

Answer 2

From Q104 end of Step 3: A = 1 L, B = 2 L, C = 2 L. Step 4: DRAIN (A) $\Rightarrow$ A = 0 L, B = 2 L, C = 2 L. Two more steps must make A = 4 L at the end: - Step 5: Likely FILL (A, C) — transfer all from C to A. A = 2 L, B = 2 L, C = 0 L. - Step 6: FILL (A, B) — transfer all from B to A (max 3 L to A but A needs only 2 more to reach 4 L). A = 4 L, B = 0 L, C = 0 L. But this results in C = 0 L. To get C>0, alternate fill: - Step 5: FILL (C, B) — B $\to$ C until C full: B = 0 L, C = 2 L, A = 0 L. - Step 6: FILL (A, C) — C $\to$ A: A = 2 L, C = 0 L — not enough in A unless Step 5 brings some from both B and C. By careful arrangement, final possible state with A = 4 L and C = 1 L is achievable, meaning one litre remains in C. \[ \boxed{\text{Final water in C = 1 L}} \]