There are three same-sized balls of different weights and colours: Red, Orange and Green. You can use the pan balance for it but cannot use weights. How will you find which one is the heaviest and which one is the lightest?
Step 1: Place the Red ball on the left pan and the Orange ball on the right pan.
Step 2: Observe which side goes down - that ball is heavier.
Step 3: Compare the heavier ball from Step 2 with the Green ball.
Step 4: If Green is heavier, then Green is the heaviest, and the lighter ball from the first comparison is the lightest.
Step 5: If Green is lighter, then the heavier ball from the first comparison is the heaviest, and Green might be the lightest.
Step 6: Compare the remaining two balls to confirm which is lightest.
Conclusion: This requires 2-3 weighings to determine both the heaviest and lightest balls.
Explanation
The chapter presents a more complex puzzle where all three balls have different weights. To find both the heaviest and lightest, we need multiple comparisons. By systematically comparing balls and tracking which is heavier in each comparison, we can rank all three balls from heaviest to lightest.
Solution Steps
Step 1: Compare Red and Orange balls on the balance.
Step 2: Note which ball is heavier. Let's say Red is heavier than Orange.
Step 3: Compare Red with Green.
Step 4: If Red is heavier than Green, Red is the heaviest. Then compare Orange and Green to find the lightest.
Step 5: If Green is heavier than Red, Green is the heaviest. Then Red is in the middle, and Orange is the lightest.
Step 6: Continue comparisons until all three balls are ranked.