In case the weights are placed on only one side of the scales,the weight of the item being weighed will be the total of the weights placed on that side.If the weights are placed on both sides,the weight will be the sum of weights placed on opposite side less the sum of weights placed by the side of the item.
You will be surprised the weights required will be the numbers formed by repeatedly multiplying 1 with 3,viz 1,3,9,27,81,243,729 ......etc
Thus if the item weighs 60 gm,you will have to work out how you can get 60 by adding or subtracting those numbers.You will find 60=81-27+9-3.Thus weights 27 and 3 are placed by the side of the item weighed and 81 and 9 placed on the opposite side.
Similarly for any item weighed.
For item weighig 301 gm,you will find 301=243+81-27+3+1.So you have to place weight 27 by the side side of the item weighed and all others on the opposite side.
Try finding what and how the weights are to be placed for items weighing 400 and 368.A tricky exercise.
You will be surprised the weights required will be the numbers formed by repeatedly multiplying 1 with 3,viz 1,3,9,27,81,243,729 ......etc
Thus if the item weighs 60 gm,you will have to work out how you can get 60 by adding or subtracting those numbers.You will find 60=81-27+9-3.Thus weights 27 and 3 are placed by the side of the item weighed and 81 and 9 placed on the opposite side.
Similarly for any item weighed.
For item weighig 301 gm,you will find 301=243+81-27+3+1.So you have to place weight 27 by the side side of the item weighed and all others on the opposite side.
Try finding what and how the weights are to be placed for items weighing 400 and 368.A tricky exercise.
400 = 729 - 243 - 81 - 9 + 3 + 1
ReplyDelete368 = 729 - 243 - 81 - 27 - 9 - 1
It was more by trial and error. Is there a more elegant method to find the sequence? is it some geometric progression?