2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44
Help the clerk of the magic shop quickly weigh the required ingredient for the potion.
A good wizard wants to prepare a potion to heal the villagers from a mysterious evil eye. It has all the ingredients it needs, except for dried lacewings. After them, he goes to the magic shop.
The seller just has a 9-kilogram bag of these insects. And also scales with bowls and weights for weighing. The wizard rejoices and asks to pour him 2 kg of lacewings - no more, no less. Accuracy is important, otherwise the healing potion will turn into poison.
The seller is stubborn and declares that he will be tortured to measure the order, because he has only two weights in the shop: for 200 g and 50 g. We will have to weigh eight times! The wizard does not share his pessimism and claims that it can be done in three weighings. Is he right or is he confusing something?
Moreover, the magician is sure that in three weighings it is possible to measure 2 kg, using only a weight of 200 g. Is this possible?
Deal with both cases.
The magician is right: three weighings are enough. Here's how the seller should proceed:
1. First weighing: divide the bag with lacewings so that there is 4.5 kg on each scale. Put half of the insects back into the bag.
2. Second weighing: Divide the remaining 4, 5 kg in half in the same way. There should be 2, 25 kg on each scale. You don't need to put anything into the bag, both parts remain on the scales.
3. Third weighing: Place both weights on one pan. This bowl will immediately outweigh the other. The seller needs to remove the lacewing from her until the sides are balanced. When this happens, on one bowl there will be 2.25 kg of insects, on the other - 2 kg of goods and weights of 200 g and 50 g. The seller needs to pick up the measured 2 kg and give it to the buyer.
The magician is right in the second case: 2 kg can be measured in three weighings, using only one weight in 200 g. The seller needs to do the following:
1. First weighing: put a 200 g weight on one bowl and divide the lacewing bag so as to balance the sides. When this happens, on one bowl there will be 4.6 kg of insects, on the other - 4.4 kg of goods and a weight of 200 g. 4. 6 kg of lacewings must be poured back into the bag.
2. Second weighing: Divide 4, 4 kg in half so that on each scale there is 2, 2 kg. You don't need to put anything into the bag, both parts remain on the scales.
3. Third weighing: put a 200-gram weight on one of the bowls, this side will immediately outweigh the other. The seller needs to remove the lacewing from here until the bowls are balanced. When this happens, one of them will have 2, 2 kg of insects, on the other - 2 kg of goods and a weight of 200 g. The seller needs to pick up the measured 2 kg and give it to the wizard.
Voila! The villagers will be saved!
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