Re:A puzzle to work on during the next two weeks: The scales problem

 First of all, here are the keynotes of the questions: 

1. we have 4 weights in total and they are all different weights. 

2. the 4 weights will have different combinations that weight herbs weight form 1-40 grams

Here are my thoughts, 

1. To measure 1 gram of herbs, there must be a 1-gram weight since that's the smallest weight possible. 

2. To measure 2 grams of herbs, we can put 2 grams of herbs and 1 gram of weight on one side and the other side must be a 3-gram weight. So, we have a 3-gram weight as our second weight. 

3. To measure 3 grams of herbs, we have a 3-gram weight. 

4. To measure 4 grams of herbs, we have 1+3 gram weights. 

5. To measure 5 grams of herbs, we have 1+3 grams but we need another 1-gram weight which doesn't work as we only have 1 1-gram weight. So basically, we have 5 grams of herbs and 1+3 grams of weight on one plate which is 9 grams in total. In order to balance the plate, we will have to have a 9-gram weight. So, we have a 9-gram weight as our third weight. 

6. To measure 6 grams of herbs,  6-gram herbs + 3-gram weight=9-gram weight 

7. To measure 7 grams of herbs, 7-gram herbs + 3-gram weight = 9-gram weight + 1-gram weight 

8. To measure 8 grams of herbs, 8g Herbs + 1g Weight=9g Weight 

9. To measure 9 grams of herbs, we have a 9-gram weight 

10. To measure 10 grams of herbs, 9-gram herbs=9-gram weight + 1-gram weight 

11. To measure 11 grams of herbs, 11g Herbs +1g Weight = 9g Weight + 3g Weight 

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14. To measure 14 grams of herbs, we have 14g herbs + 3g Weight +1g Weight+9g Weight = 27g which means we will have a 27-gram weight as our third weight. 

Similarly, we can use a similar method to weight the rest of the possible herb weights from 15g-40g. 

To students, I would ask if they have any other method to solve the puzzle using mathematical calculations. How many grams of herbs does the seller need to have minimally to make this calculation possible.