# What four weights can be used to balance from 1 to 30 pounds?

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posted Jan 3
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A merchant has a 40 kg weight which he used in his shop. Once, it fell from his hands and was broken into 4 pieces. But surprisingly, now he can weigh any weight between 1 kg to 40 kg with the combination of these 4 pieces.

So question is, what are weights of those 4 pieces..?

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?

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We have two soap of equal weights and a 3/4 pound weight.
The balance was equal when we placed one soap on one side and 3/4 pound weight and 3/4th soap on another side.

What is the weight of soap?

Fill in the boxes with numbers from 1-10. One number can be used only once.