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4newton
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you are right. I just thought of that today and was going to change it. thanks for getting that.
Iron Monger Weighs Goods up to 40lb in 1lb Increments
- Context: Undergrad
- Thread starter Ian Rumsey
- Start date
Click For Summary
Discussion Overview
The discussion revolves around the problem of determining the minimum number of cuts required to create weights from a 40lb iron bar, allowing for the weighing of goods up to 40lb in 1lb increments. Participants explore various cutting strategies and mathematical approaches to achieve this goal.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants suggest that 11 cuts can achieve the goal by making four equidistant lengthwise cuts and seven right angle crosscuts.
- Others propose that 8 cuts can be made by cutting the bar into segments like a pizza and then further dividing them.
- One participant claims that only 3 cuts are needed to create weights of 1, 3, 9, and 27, or alternatively, 2 cutting actions could suffice if arranged correctly.
- Another participant discusses the optimal choice of weights for generating integers, suggesting that the smallest set is {1, 2, 4,...} for one pan and {1, 3, 9,...} for both pans.
- Some participants explore the concept of balanced ternary and how it relates to the number of weights needed for measuring various amounts.
- There are claims that only 2 orthogonal cuts can yield the necessary weights, with discussions about the implications of cutting actions versus the number of cuts made.
- Some participants question the uniqueness of the powers of three as an optimal solution, suggesting alternative combinations that also cover the required weights.
Areas of Agreement / Disagreement
Participants express a range of views on the minimum number of cuts required, with no consensus reached. Multiple competing methods and interpretations of the cutting strategy are presented, leading to ongoing debate.
Contextual Notes
Some discussions highlight the dependence on definitions of cuts and cutting actions, as well as the mathematical principles underlying the proposed solutions, which remain unresolved.
Who May Find This Useful
This discussion may be of interest to those studying mathematical problem-solving, combinatorial optimization, or anyone interested in practical applications of weights and measurements in physics or engineering contexts.
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