# Finding the heavier ball | Summary and Q&A

63.4K views
July 15, 2014
by
Khan Academy
Finding the heavier ball

## TL;DR

Using a scale, determine the heaviest ball out of nine identical balls in a minimum number of weighings.

## Key Insights

• #️⃣ The minimum number of weighings required is two, regardless of the number of balls.
• 💬 By ruling out 2/3 of the balls in each weighing, the heavier ball can be identified.
• 💬 The process can be applied to different scenarios, such as having 27 balls or a different number of balls.

## Transcript

we have nine balls right over here and we're going to assume that they look completely identical but one of the balls is slightly heavier than the other eight and you can't tell it just by feeling it's very slightly heavier you would need some type of an instrument to tell which whether the ball one one ball is heavier than another ball and the onl... Read More

## Questions & Answers

### Q: How many weighings are needed to find the heavier ball out of nine identical balls?

The minimum number of weighings required is two, as explained in the content.

### Q: How does the first weighing help in narrowing down the heavier ball?

The first weighing, with three balls on each side, helps determine if the heavier ball is in the group of three or not.

### Q: What should be done after a balanced first weighing?

If the first weighing is balanced, one ball from the group of three is weighed against another ball to identify the heavier one.

### Q: What if the first weighing shows an imbalance?

In case of an imbalance in the first weighing, further weighings are done with the heavier side to narrow down the heaviest ball.

## Summary & Key Takeaways

• There are nine identical balls, one of which is slightly heavier.

• A scale is the only instrument available to determine the heavier ball.

• By weighing groups of balls and ruling out 2/3 each time, the heavier ball can be identified in two weighings.

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