You have a weighing balance, which you can place weights on both sides of. You need to measure all weights between 1 and 1000.
For example if you have weights 1 and 3, you can measure test objects of weights 1, 3 or 4. You can also measure objects of weight 2, by placing 3 on one side and 1 on the side which contain the object to be weighed.
What is the minimum number of weights that you would need to be able to measure all (integral) weights from 1 kg to 1000 kg?
1, 3, 9, 27, 81, 243, 729 kgs weights in different combinations will be able to weigh in the given range. Like for 1000 kgs, 729 + 243 + 27 + 1 = 1000 kgs, for 997 kgs, 729 + 243 + 27 + 1 on one pan & 3 kg on the other pan.
This is simply the numbers 2^0,2^1,2^2 ... that is 1,2,4,8,16... So for making 1000 kg we need up to 1, 2, 4, 8, 16, 32, 64, 128, and 512
An apple seller is hosting a competition. He offers 1000 apples and 10 boxes to the people who pass by. The challenge is to put those 1000 apples in the 10 boxes in such a manner that if he asks for any amount of apples, the person is able to directly give him the boxes or a combination of boxes. If the person can do it, he promises to give a thousand apples for free.
If you happen to pass by the apple seller, will you be able to win a thousand apples?
