Suppose you have five balls that are labeled \"A\", \"B\", \"C\", \"D\", \"E\".

Question

Suppose you have five balls that are labeled "A", "B", "C", "D", "E". You also have six cups labeled sequentially "0", "1", "2", "3", "4", "5". These cups are glued to a flat board, so they cannot be removed or rearranged. The balls are placed in the cups in a specific order. The first cup is empty. The initial state Si looks like this: The balls are moved from cup to cup. The final state Sf looks like this: Basically, the order of the balls in the cups needs to be reversed. Write a detailed and complete list of ball move instructions to go from the initial state Si to the final state Sf under the following constraints: A cup can contain at most one ball at a time. The rearranging of the balls in the cups is accomplished by consecutive move operations. A move operation consists of moving a single ball from its current cup to an empty cup. A ball may jump over at most one other ball in a single move, and only if there is an empty cup available on the other side.

Explanation / Answer

move ball in cup 2 to cup 0

move ball in cup 1 to cup 2

move ball in cup 3 to cup 1

move ball in cup 2 to cup 3

move ball in cup 4 to cup 2

move ball in cup 3 to cup 4

move ball in cup 5 to cup 3

move ball in cup 4 to cup 5

move ball in cup 3 to cup 4

move ball in cup 2 to cup 3

move ball in cup 1 to cup 2

move ball in cup 0 to cup 1 //_BCDEA will be there

move ball in cup 2 to cup 0

move ball in cup 1 to cup 2

move ball in cup 3 to cup 1

move ball in cup 2 to cup 3

move ball in cup 4 to cup 2

move ball in cup 2 to cup 4

move ball in cup 2 to cup 3

move ball in cup 1 to cup 2

move ball in cup 0 to cup 1 //_CDEBA will be there

move ball in cup 2 to cup 0

move ball in cup 1 to cup 2

move ball in cup 3 to cup 1

move ball in cup 2 to cup 3

move ball in cup 1 to cup 2

move ball in cup 0 to cup 1 //_DECBA will be there

move ball in cup 2 to cup 0

move ball in cup 1 to cup 2

move ball in cup 0 to cup 1 //_EDCBA will be there i.e. final state

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.