Assume that you have a block weighing 40 kg and have tools to divide it as you want. Now, your task is to cut that block into 4 pieces such that only using those 4 pieces and a two-way balancing pan, you can measure any weight from 1 kg to 40 kg ? (You should be able to measure any weight like 1 kg, 2 kg, 3 kg upto 40 kg ).
Now since you have to divide it only into 4 pieces, so dividing it into 1, 2, 4 and 8 kg will not serve the task, as they will not be able to measure all the weights upto 40 kg.
So, what we can do is divide it into 4 blocks of weights 1 kg, 3 kg, 9 kg and 27 kg. Now, see how we can measure all the weights using it:
1 kg: 1 kg can be measured directly using block of 1 kg.
2 kg: To measure 2 kg, we can put 1 kg block with 2 kg and then put 3 kg block against these two, i.e., 2 + 1 = 3.
Similarly, 5 kg : It can be done using 5 kg + 1 kg + 3 kg = 9 kg.
7 kg : 7 kg + 3 kg = 1 kg + 9 kg.
Like this we can do for all the weights till 40 kg (40 = 1 + 3 + 9 + 27). Hence, the 4 weights required are 1 kg, 3 kg, 9 kg and 27 kg.
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