In detail

The balance problem

The balance problem

A seller has 32 kilos of flour and a scale of dishes like the one in the image but no weight. A customer wants to buy exactly 10 kilos of flour. How does the seller have to proceed to satisfy the customer with the minimum number of weights?

Solution

You must make 4 heavy. First you have to distribute all flour in both dishes until you balance the balance with what you will get two 16Kg piles. Repeat the same process with one of the 16Kg piles that you have obtained so that when balancing the balance you will have 8Kg on each plate. Again, take one of the 8Kg piles and distribute them in the scales until you get two 4Kg piles. Finally, distribute the 4Kg in the two saucers so that when the balance is in balance it will have 2Kg in each plate. Now you simply have to deliver one of the piles of 8Kg and another of 2Kg to meet customer requests.