A market vendor sells dried cooking herbs in whole-number amounts from 1 to 40 grams. The vendor has an old fashioned two pan weigh scale, and has exactly four weights of different amounts that allow them to weight out any of these amounts of herbs--without using the herb or any other object as an auxiliary weight.
According to me the values for 4 weights should be 1,2,5,10. When I saw this problem, it reminds me of Indian weight system. Most of the vendors in small cities use two pan weight scale to sell their fruits and vegetables. Although they have more weights, and their weights usually include 1,2,3,5,10,20,50,100. According to me suitable weights those add up to the numbers from 1 to 40 are 1,2,5 and 10. I didn't take 3 because to get 3 we can add 1 and 2 together.
1,2,5 and 10 can add to get any value up to 40. For instance
1gm= 1gm
2gm=2gm
3gm=1+2
4gm= 1+2=3 and again plus 1gm
5gm=5gm
6gm= 5+1
7gm= 5+2
8gm= 5+2+1
9gm= 5+2+1=8 plus 1gm more
10gm= 10gm
11gm= 10+1
12gm=10+2
13gm= 10+2+1
14gm= 10+2+1 plus 1gm more
15gm= 10+5
it would continue like 10 more than as from 1 to 10
we have to add 10 twice to the calculations from 1 to 10 to get the numbers between 20 and 30, and thrice for numbers from 30 to 40. For instance, 37=10+5+7 once and again add 10 two more times. It is possible to get any number between 1 to 40 by using these four numbers.
Are there several correct solutions?
Yes, there might be several correct solutions to this problem. The other numbers should be 1,3,5 and 10 or 1, 2, 10, and 20. But according to me one number must be 1 and the second number must be either 2 or 3.
Extension to this problem
What should be the 4 weights if the vendor wants to sell dried cooking herbs in whole numbers amount from 1 to 100 grams? Could you use the same weights as you used for 1 to 40 grams? why or why not?
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