How many weighings of a balance scale are needed to find a lighter counterfeit c
ID: 3120192 • Letter: H
Question
How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to find the lighter coin using this number of weighings.
How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to find the lighter coin using this number of weighings.
How many weighings of a balance scale are needed to find a lighter counterfeit coin among four coins? Describe an algorithm to find the lighter coin using this number of weighings.
Explanation / Answer
Take 2 of these 4 coins and plac them in different weight pans of a balane scale. If the lighter one is among these two that respective pan will go up. If the lighter coin isn't in these two then repalce these two coins with the 3rd and 4td coin. The lighter one will definitely be amognst this two and we will know it ocne it is placed on the balance scale.
Thus it will take us a minimum of 1 weighings and maximum of 2 weighings.
Thus in general you start by dividing the number of coins into groups of 2 or 3 (of equal sizes) and proceed accordingly. If in case of groups of 3, start with choosing any 2 groups and see if any of them is wieghing lighter, else the lighter coin will be in group 3. Now, for the particualr group, repeat the process of dividing into sub-groups of 2 or 3 (depedning upon the total number) and proceed in the same way.
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