The 12 Weights Riddle

The 12 Weights Riddle ⚖️

You have 12 identical-looking balls, but one of them is slightly heavier than the others. You have a balance scale, but you can only use it 3 times to find the heavier ball.

How do you find the heavier ball in just 3 weighings?

Hint:

You can divide and conquer! Instead of trying to compare all the balls at once, divide the 12 balls into groups and use the balance scale to eliminate groups as possibilities.

Think of it as a process of elimination by splitting them into three smaller groups and weighing them in a way that narrows down the possibilities each time.

Answer:

The Strategy: Divide and Conquer

You can solve this puzzle by dividing the 12 balls into 3 groups of 4 balls each. Here’s how to find the heavier ball in just 3 weighings:

Weighing 1:

Divide the 12 balls into 3 groups of 4 balls each.
- Group 1: 4 balls
- Group 2: 4 balls
- Group 3: 4 balls
Weigh Group 1 against Group 2.
- Case 1: If one side is heavier, you know the heavier ball is in the group on the heavier side.
- Case 2: If both sides are equal, the heavier ball must be in Group 3.

Weighing 2:

Now that you have narrowed it down to a group of 4 balls, divide this group of 4 balls into 3 groups:

1 ball, 1 ball, and 2 balls.

Weigh 1 ball against 1 ball.
- Case 1: If one ball is heavier, that’s your heavier ball.
- Case 2: If both are equal, then the heavier ball is in the group of 2 balls.

Weighing 3:

Now that you’ve narrowed it down to just 2 balls, you only need to compare them directly:

Weigh the 2 remaining balls against each other.
- The heavier ball will be the one that tips the scale.

Final Answer:

You’ll have found the heavier ball after 3 weighings! 🏆

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