Hi all,
I have not finished the entire question yet and this is what my method would be for the first part based on my interpretation of the word problem.
"has exactly four weights of different amounts that allows them to weigh out any of these amounts of herbs -- without using the herbs or any other object as an auxiliary weight"
Auxiliary : providing supplementary or additional help and support
For me i am using the herbs to get only the end result so my scales are void of product when I am done as the product goes to the customer. [I felt i should define this in support of my method]
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weights of 1 2 5 10
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Results: w = wight | h = herbs
1w= 1h
2= 2
3= 2+1
4= 5-1
6= 5+1
7= 5+2
8= 5+2+1
9= 10-1
10= 10
11= 10+1
12= 10+2
13= 10+2+1
14= 10+5-1
15= 10+5
16= 10+5+1
17= 10+5+2
18= (2x10) - 2
Step 1: 10w = 1w + herbs
Step 2: remove 10w and 1 w
step 3 : add herbs to balance scale and yield is exactly 18
Etc... This process can be done in different increments for 19-40
19= (2x10) - 1
20= (2x10); use one 10w balance with herbs then remove the re-balance by adding herbs
step:1 10w = 10h,
step2: remove 10w and balance by adding 10h
step 3: add 2w and balance with 2h
step 4 remove 2w and yield is exactly 22h
Etc... [the process is completed in a similar fashion for all amounts 19-40]
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Hi TsáKtalay’pa, and thanks for posting part of your process in solving this puzzle! Your weights of 1, 2, 5 and 10 work well up to 18, but I can't see how you could go above 18 with them. There is a constraint in the problem: you are not allowed to use bundles of herbs to create extra 'weights'! You are only allowed to use the four metal weights, not the herbs themselves (to make the problem interesting --- because otherwise, you could weigh ANY amount with a single 1 gram weight and then bundles of herbs calibrated to 2, 3, 4, 5, ... , as high as you want, which is not mathematically interesting or challenging!) See if you can move forward with just four metal weights.
ReplyDeleteGood morning, thank you for your words and yes I will move forward. I apologize in advance for disagreeing with you but to me this is the point of education, forward movement through debate.
ReplyDeleteI do disagree with your statement and had provided an interpretation of the word problem. Please know that I believe there are multiple methods for a solution. And when I had developed mine I had shared with others it is 'a' method.
The word problem as presented was designed such that it must be clarified. In my current studies word problems are a topic and as I will be working in a multi-lingual educational system wording is crucial in the promotion of education and independent learning. If a narrow or singular result was required the wording of the problem should reflect that and I believe it does not. [I spent a career in engineering design and a method of problem solving is using multiple perspectives to design a solution and I picked a perspective within the bounds of the given words]
The comparison of a 1 gram weight to what I did is not the same. The analogy of 1 weight, for all means the 1 weight would be used multiple times in the process. Where as my method does not use the weight(s) more than once.
“you are not allowed to use bundles of herbs to create extra 'weights'!” thank for sharing this statement. I justified my method in my writings. If you feel I have not then I would enjoy the conversation to understand you better and that in turn makes me better.
I will work toward alternate solutions with the 4 weights and 2 pan scale.
Have a nice day,
TsáKtalay’pa
Thanks TsaKtalay'pa! I think I see how you're doing this, and it is certainly much more complex than simply adding multiple bundles of 1 gram of herbs. I wonder if this is a unique solution using this method... what are your thoughts on this? Thanks for thinking outside the box, and for standing up for your ideas!
ReplyDelete