There is a 40 kilogram stone that broke into 4 pieces such that you can measure any weight between 1 kilogram to 40 kilogram using a balance what are the weights of the broken pieces
There is a 40 kilogram stone that broke into 4 pieces such that you can measure any weight between 1 kilogram to 40 kilogram using a balance what are the weights of the broken pieces
First of all you can measure wt. in the balance in two ways.
- By putting the weight on one side and the object on the other side.
- By putting a higher weight or two or more weight altogether on one side and a lower weight or two or more weight s.t. the sum of those is lower than the higher weight along with the object to be measured on the other side. ( I.e. measuring by the difference between the two weights )
From my observations I have seen a similarity in these kind of problems.
Whatever the total weight. If you have to break it in pieces and then measure from that, in that case you have to find a term X s.t. 3X+1 equals the total weight of the object (in this case 40).
So here X is 13. Now write 40 in the form
13+(14+13)=40 ~ 13+27=40
Now interestingly if you can find a way to measure any weight from 1 to 13 you can measure any weight in the range 40.
If you can measure upto 13, you can measure 14 from 27 kg wt (27-13).Then you can measure any weight from 14 to 27 by putting 27 kg in one side and putting the weights in other side from 13 kg to 1 kg.
Now even you can measure 27 kg to 40 kg by putting the object on one side and putting the 27 kg combining with the other weights from 1 kg to 13 kg.
In similar way you can find how to divide the 13 kg weight in the same pattern.
Find x from 3x+1=13 I.e. x=4.
Now write 13 in the form
4+(5+4)=13 ~ 4+9=13
Similarly if you find a way to get the range of 1 to 4 kg you can measure 5 kg (9-4).
And then can measure upto 9 kg similarly by substacting and upto 13 kg in same way by addition.
To divide 4 kg in same way find x and write 4 like
1+(2+1)=4 ~ 1+3=4
Now you can see that you can find upto 4 kg by 1 and 3 kg weight.
So then we need a 9 kg wt. to measure upto 13 kg and then a 27 kg wt. to measure upto 40 kg.
Note: This I found by analysing the problem. There may be a contradiction though. But all I can say that this formulae only works for the wts in the form of 3X+1.
First of all you can measure wt. in the balance in two ways.
- By putting the weight on one side and the object on the other side.
- By putting a higher weight or two or more weight altogether on one side and a lower weight or two or more weight s.t. the sum of those is lower than the higher weight along with the object to be measured on the other side. ( I.e. measuring by the difference between the two weights )
From my observations I have seen a similarity in these kind of problems.
Whatever the total weight. If you have to break it in pieces and then measure from that, in that case you have to find a term X s.t. 3X+1 equals the total weight of the object (in this case 40).
So here X is 13. Now write 40 in the form
13+(14+13)=40 ~ 13+27=40
Now interestingly if you can find a way to measure any weight from 1 to 13 you can measure any weight in the range 40.
If you can measure upto 13, you can measure 14 from 27 kg wt (27-13).Then you can measure any weight from 14 to 27 by putting 27 kg in one side and putting the weights in other side from 13 kg to 1 kg.
Now even you can measure 27 kg to 40 kg by putting the object on one side and putting the 27 kg combining with the other weights from 1 kg to 13 kg.
In similar way you can find how to divide the 13 kg weight in the same pattern.
Find x from 3x+1=13 I.e. x=4.
Now write 13 in the form
4+(5+4)=13 ~ 4+9=13
Similarly if you find a way to get the range of 1 to 4 kg you can measure 5 kg (9-4).
And then can measure upto 9 kg similarly by substacting and upto 13 kg in same way by addition.
To divide 4 kg in same way find x and write 4 like
1+(2+1)=4 ~ 1+3=4
Now you can see that you can find upto 4 kg by 1 and 3 kg weight.
So then we need a 9 kg wt. to measure upto 13 kg and then a 27 kg wt. to measure upto 40 kg.
Note: This I found by analysing the problem. There may be a contradiction though. But all I can say that this formulae only works for the wts in the form of 3X+1.
