Weight of Heavy Ball | Puzzles for Interview - Interview Preparation PDF Download

Introduction

If you have 2187 balls and need to find the heaviest one, here is a step-by-step guide to help you do it in a minimum number of attempts.

Solution

Step 1: Divide the Balls into 3 Groups of 729 Each
Divide the 2187 balls into three equal groups of 729 each and label them C1, C2, and C3. Place C1 on one side of the weighing machine and C2 on the other. This will give rise to three conditions, which are:

• Condition 1: C1 equals C2, meaning C3 has the heaviest ball.
• Condition 2: C1 is less than C2, meaning C2 has the heaviest ball.
• Condition 3: C1 is greater than C2, meaning C1 has the heaviest ball.

Suppose Condition 1 follows up, and C3 has the heaviest ball.

Step 2: Divide C3 into 3 Groups of 243 Each

Divide C3 again into three equal groups of 243 each, naming them again C1, C2, and C3. Place C1 on one side of the weighing machine and C2 on the other. This can give rise to three conditions:

• Condition 1: C1 equals C2, meaning C3 has the heaviest ball.
• Condition 2: C1 is less than C2, meaning C2 has the heaviest ball.
• Condition 3: C1 is greater than C2, meaning C1 has the heaviest ball.

Suppose Condition 2 follows up, and C2 has the heaviest ball.

Step 3: Divide C2 into 3 Groups of 81 Each

Divide C2 again into three equal groups of 81 each, naming them again C1, C2, and C3. Place C1 on one side of the weighing machine and C2 on the other. This can give rise to three conditions:

• Condition 1: C1 equals C2, meaning C3 has the heaviest ball.
• Condition 2: C1 is less than C2, meaning C2 has the heaviest ball.
• Condition 3: C1 is greater than C2, meaning C1 has the heaviest ball.

Suppose Condition 3 follows up, and C1 has the heaviest ball.

Step 4: Divide C1 into 3 Groups of 27 Each

Divide C1 again into three equal groups of 27 each, naming them again C1, C2, and C3. Place C1 on one side of the weighing machine and C2 on the other. This can give rise to three conditions:

• Condition 1: C1 equals C2, meaning C3 has the heaviest ball.
• Condition 2: C1 is less than C2, meaning C2 has the heaviest ball.
• Condition 3: C1 is greater than C2, meaning C1 has the heaviest ball.

Suppose Condition 3 follows up, and C1 has the heaviest ball.

Step 5: Divide C1 into 3 Groups of 9 Each

Divide C1 again into three equal groups of 9 each, naming them again C1, C2, and C3. Place C1 on one side of the weighing machine and C2 on the other. This can give rise to three conditions:

• Condition 1: C1 equals C2, meaning C3 has the heaviest ball.
• Condition 2: C1 is less than C2, meaning C2 has the heaviest ball.
• Condition 3: C1 is greater than C2, meaning C1 has the heaviest ball.

Suppose Condition 1 follows up, and C3 has the heaviest ball.

Step 6: Divide C3 into 3 Groups of 3 Each

Divide C3 again into three equal groups of 3 each, naming them again C1, C2, and C3. Place C1 on one side of the weighing machine and C2 on the other. This can give rise to three conditions:

• Condition 1: C1 equals C2, meaning C3 has the heaviest ball.
• Condition 2: C1 is less than C2, meaning C2 has the heaviest ball.
• Condition 3: C1 is greater than C2, meaning C1 has the heaviest ball.

Suppose Condition 1 follows up, and C3 has the heaviest ball.

Step 7: Divide C3 into 1 Group of 1

Finally, divide C3, which has three balls, into a group of 1, naming them again B1, B2, and B3. Place B1 on one side of the weighing machine and B2 on the other. This can give rise to three conditions:

• Condition 1: B1 equals B2, meaning B3 has the heaviest ball.
• Condition 2: B1 is less than B2, meaning B2 has the heaviest ball.
• Condition 3: B1 is greater than B2, meaning B1 has the heaviest ball.

Suppose Condition 1 follows up, then B3 is the heaviest ball.

Conclusion

By following these seven steps, you can find the heaviest ball out of 2187 balls in a minimum number of attempts. The number of attempts required is equal to 7 times, which is the cube of 3 (i.e., 3^7).