To find the heavier marble using a balance scale only twice, you can follow the process below:
1. Divide the marbles into three groups: Group A with 3 marbles, Group B with 3 marbles, and Group C with 1 marble.
2. First use of the balance scale: Compare the weights of Group A and Group B.
Case 1: If Group A and Group B weigh the same, then the heavier marble is in Group C.
Case 2: If either Group A or Group B is heavier, the heavier marble must be in the heavier group.
3. For Case 2, let’s assume that Group A is the heavier group (if Group B is heavier, the same approach will apply). Now, we have three marbles in Group A, and we want to use the balance scale one more time.
4. Divide Group A into three subgroups: Marble 1, Marble 2, and Marble 3.
5. Second use of the balance scale: Compare the weights of Marble 1 and Marble 2.
Case 2A: If Marble 1 and Marble 2 weigh the same, then Marble 3 is the heavier marble.
Case 2B: If either Marble 1 or Marble 2 is heavier, the heavier marble is the heavier one in the comparison.
By following this process, you can identify the heavier marble by using the balance scale only twice.