The 9 Balls Puzzle: How to Solve It

The 9 balls puzzle is a classic logic problem that involves determining a heavier or lighter ball from a set of nine. It's a fun and challenging puzzle that can test your problem-solving skills and logical reasoning.

The Puzzle

Here's how the puzzle works:

• You have 9 identical-looking balls.
• One of the balls is either heavier or lighter than the rest.
• You have a balance scale to weigh the balls.
• Your goal is to identify the odd ball and whether it's heavier or lighter in just three weighings.

The Solution

Here's a step-by-step solution to the 9 balls puzzle:

Weighing 1:

1. Place 3 balls on each side of the balance scale (balls 1, 2, 3 on one side and balls 4, 5, 6 on the other).
2. Possible outcomes:
   • The scale balances: The odd ball is among balls 7, 8, or 9. Proceed to Weighing 2a.
   • One side is heavier: The odd ball is among balls 1, 2, or 3 (if the left side is heavier) or balls 4, 5, or 6 (if the right side is heavier). Proceed to Weighing 2b.

Weighing 2a (Scale Balanced in Weighing 1):

1. Place ball 7 on one side of the scale and ball 8 on the other.
2. Possible outcomes:
   • The scale balances: Ball 9 is the odd ball. Proceed to Weighing 3a.
   • One side is heavier: The heavier ball is the odd ball. Proceed to Weighing 3a.
   • One side is lighter: The lighter ball is the odd ball. Proceed to Weighing 3a.

Weighing 2b (One Side Heavier in Weighing 1):

1. Take the group of 3 balls that was heavier (or lighter, depending on the outcome of Weighing 1) and place 1 ball on each side of the scale (for example, ball 1 on one side and ball 2 on the other).
2. Possible outcomes:
   • The scale balances: The remaining ball (ball 3 in this example) is the odd ball. Proceed to Weighing 3b.
   • One side is heavier: The heavier ball is the odd ball. Proceed to Weighing 3b.
   • One side is lighter: The lighter ball is the odd ball. Proceed to Weighing 3b.

Weighing 3a (Odd Ball Identified in Weighing 2a):

1. Take the odd ball from Weighing 2a and any other ball from the original set (for example, ball 1).
2. Place the odd ball on one side of the scale and the other ball on the other side.
3. Possible outcomes:
   • The scale balances: The odd ball is the same weight as the other balls (this scenario is impossible if the puzzle is set up correctly).
   • The odd ball is heavier: The odd ball is heavier than the other balls.
   • The odd ball is lighter: The odd ball is lighter than the other balls.

Weighing 3b (Odd Ball Identified in Weighing 2b):

1. Take the odd ball from Weighing 2b and any other ball from the original set (for example, ball 4).
2. Place the odd ball on one side of the scale and the other ball on the other side.
3. Possible outcomes:
   • The scale balances: The odd ball is the same weight as the other balls (this scenario is impossible if the puzzle is set up correctly).
   • The odd ball is heavier: The odd ball is heavier than the other balls.
   • The odd ball is lighter: The odd ball is lighter than the other balls.

Tips for Solving the Puzzle

• Visualize: It can be helpful to draw a diagram or picture of the balls and the scale to keep track of the weighings.
• Eliminate possibilities: As you weigh the balls, eliminate possibilities to narrow down the potential odd ball.
• Practice: The more you practice, the easier it will become to solve the 9 balls puzzle.

Conclusion

The 9 balls puzzle is a classic problem-solving challenge that requires logical reasoning and strategic thinking. By following the steps outlined above, you can successfully identify the odd ball and determine whether it's heavier or lighter within three weighings. So grab some balls, a balance scale, and put your puzzle-solving skills to the test!