Somewhere around in SA 1500, Sauron gave away six power rings to Dwarf-kings. Al
ID: 3711408 • Letter: S
Question
Somewhere around in SA 1500, Sauron gave away six power rings to Dwarf-kings. All of those six rings were equal in weight. One of the Elve kings (Celebrimbor) gave another ring to Dwarf-kings which was identical to the six power rings, but it was slightly lighter than the original six. Let’s assume after a few centuries descendants of Dwarf-kings wants to find out which one of the seven rings was the one given by the Elve king. Your task is to help them to figure it out using your knowledge of decision trees. You use a weighing scale (from middle earth) that can weigh only twice. In other words, There are six identical rings with the same weight and another identical ring with less weight. If all the seven rings are mixed, how to use a balance to find the one ring with less weight in two weighings? Note: You will have to draw a decision tree Hint: One node can represent left and right hand side of a weighing scale and its children can represent a node based on the result of weighing scale
Explanation / Answer
Consider the six power rings numbered 1,2,3,4,5,6 of equal weight
7th ring which is identical to above six and having less weight
The idea is
Total rings set = {1,2,3,4,5,6,7}
No. of weighings=2
place any three rings on one side and the three rings on the other side
Conditions :
1. if three rings on left equals the weight of three rings on right, then the one that is not placed in the wieghts will be the required one i.e, ring given by Elve king
2. if three rings on left not equals the weight of three rings on right, then consider the three having less weight either on left hand side or right hand side
3. Take two from the three rings having lesser weight and place them on the weighings again
3.1 if the two rings wieghts the same, then the one which is not placed is the Elve king's ring
3.2 if the twi rings weights different, the one with lesser weight is Elve King;s Ring
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