you have 13 bags of gold wins. out of 13 bags gold coins, there is one bag gold coins lighter. assume that one real gold coins is 10g and the fake is 9g. now, you are given a electronic beam balance. find the most minimum ways to figure out which bag of gold coins is lighter.
To find the lighter bag of gold coins, you can use the electronic beam balance. Here's the step-by-step process to identify the lighter bag with the minimum number of weighings:
1. Number the bags from 1 to 13 for convenience.
2. Let's use a binary search strategy to quickly narrow down the possibilities. Start by dividing the 13 bags into three groups: A, B, and C.
- Group A: Bags 1 to 4
- Group B: Bags 5 to 8
- Group C: Bags 9 to 13
3. First, compare the weights of Group A and Group B on the balance.
- If the weights are the same, the lighter bag is in Group C. Discard Groups A and B, and proceed to step 4 with the five remaining bags.
- If either Group A or Group B is lighter, the lighter bag is within that group. Take the lighter group and divide it into three smaller groups, repeating the process.
4. For the remaining five bags, label them as Group X: Bags 1 to 2, Group Y: Bags 3 to 4, and Group Z: Bag 5.
- Compare the weights of Group X and Group Y.
- If the weights are the same, the lighter bag is Bag 5.
- If either Group X or Group Y is lighter, the lighter bag is within that group. Take the lighter group and proceed to step 5 with two remaining bags.
5. For the two remaining bags, weigh them against each other.
- If one bag is lighter, that is your answer.
- If both bags weigh the same, the last remaining bag is the lighter one.
In summary, you can find the lighter bag with a maximum of three weighings: one for the initial division, one for the second division, and one final weighing.