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...
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.
2 answers
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.
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.
1 answer