Question

Dr NIM is a game from the 1960s that plays a version of the game of Nim against a human opponent. In this version of Nim, each player must take away 1, 2, or 3 marbles on her turn. The player who takes the last marble loses. Describe your strategy to win the game against a clever opponent if the game started with your turn and 6 marbles.

Answer 1

Answer:

Throughout all situations, we'll win if we pick 1 marble during our first turn. A further explanation is given below.

Step-by-step explanation:

Whether there are six marbles anywhere, and that it's our task or job.

We have to always be confident that there ought to be at least two marbles or more and 4 marbles because we have the last step, as we will therefore ensure our pass and leaving 1 marble behind. After all, the competitor will lose.

Therefore, if we taking out 1 marble out of 6, 5 would be left. And either 1, 2, and 3 marbles ought to be removed by the opponent.

• Case 1 - Opponent takes away 1 marble

Then, with just 4 marbles left, we'll have our turn. We would carry 3 of them away as well as the opponent will have 1 marble remaining and we can draw.

• Case 2 - Opponent takes away 2 marbles

And, with 3 marbles left, we'll have our choice. We would take 2 of those away as well as the competitor will have 1 marble remaining and then we can draw.

• Case 3 - Opponent takes away 3 marble

And, with 2 marbles remaining, we'll have our turn. We would establish previously 1 of them back as well as the competitor will have 1 marble remaining and that we can draw.

So, throughout all situations, we'll win whether we pick 1 marble after our very first turn.