You are considering buying 27 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found the counterfeit coin.
Can you explain the steps to get the answer 3.
Take two groups of 13 coins, and one left over.
If the two groups are equal, the one is counterfit.
If the two groups are not equal, take the light weight group, divide it into two groups of six. Balance them, and if equal, it is the one left over.
If they are unequal, choose the light side.
Divide it into two groups of three, take the light side, divide it into two groups of one, compare them...
Split them into 3 groups of 9
1. Place a group of 9's on either side of the scale
-If they don't balance, then you know the fake is in the group up high
if the do balance, then the fake is in the group of 9 not weighed.
2. split the group containing the fake into 3 groups of
3 and repeat the weighing process described in step 1 to determine which group of 3's contains the fake.
3rd weighing, take 2 of the coins from the group of 3 which contains the fake and weigh them
use the same argument as the one I used in step 1
3 weighings are needed.
To find the counterfeit coin among the 27 silver coins, we can use a balance scale to compare the weights of the coins. Here are the steps to determine the least number of weighings required to find the counterfeit coin:
Step 1: Divide the 27 coins into three groups of 9 coins each.
- Label these groups as Group A, Group B, and Group C.
Step 2: Weigh two of the groups, Group A and Group B, against each other on the balance scale.
- If the scale balances, the counterfeit coin is in Group C. Move to Step 3.
- If the scale tips to one side, the counterfeit coin is in the heavier group. Move to Step 3.
Step 3: Choose any three coins from the heavier group determined in Step 2.
- Remove the remaining six coins from the scale as they are not relevant anymore.
Step 4: Weigh two of the three coins chosen in Step 3 against each other on the balance scale.
- If the scale balances, the counterfeit coin is the one coin not weighed. Move to Step 5.
- If the scale tips to one side, the counterfeit coin is in the heavier group. Move to Step 5.
Step 5: Choose any two coins from the heavier group determined in Step 4.
- Remove the remaining coin from the scale as it is not relevant anymore.
Step 6: Weigh the two coins chosen in Step 5 against each other on the balance scale.
- If the scale balances, the last remaining coin is the counterfeit coin.
- If the scale tips to one side, the counterfeit coin is the heavier coin on the scale.
By following these steps, you can determine the counterfeit coin within just three weighings on the balance scale.