How Will the Son Break Off Links for 123 Weeks Without Skipping a Week?

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Discussion Overview

The discussion revolves around a brain teaser involving a son who must break off links from a chain over a period of 123 weeks. Participants are questioning the validity of the problem and exploring the implications of the required actions each week.

Discussion Character

  • Debate/contested
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the question is fundamentally flawed, suggesting that if the son must break off new links each week, it contradicts the premise of the problem.
  • One participant calculates that a minimum of 4 cuts is needed for a chain with 89 links, detailing specific links where cuts should be made to achieve certain pieces.
  • The same participant provides a breakdown of how the distribution of links occurs over the weeks, illustrating the process with a table that shows the accumulation of links given each week.
  • A later post includes an edit that appears to correct or clarify a previous statement regarding the distribution of links, although the context of the edit is not fully explained.

Areas of Agreement / Disagreement

Participants generally disagree on the validity of the original question, with some asserting it is incorrect while others attempt to analyze the problem mathematically. No consensus is reached regarding the interpretation of the problem.

Contextual Notes

The discussion includes assumptions about the mechanics of breaking links and the implications of the weekly requirements, which remain unresolved. The mathematical steps and reasoning presented may depend on specific interpretations of the problem.

MasterBlaster
Brain Teaser #4??

What is the explanation. It seems totally incorrect.

If the son is going to stay 123 weeks - and each week he HAS TO break off new links.

Then he MUST break off something each of the 123 weeks.

Explain the question...
 
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See, no one knows the answer becaue it's wrong!
 
The minimum number of cuts needed to be made is 4 for a chain with 89 links.
If the links are numbered serially from 1 to 89, then the cuts would be made on the following links:
6, 17, 38, and 79.

This would result in 4 one-link pieces, one 5-link piece, one 10-link piece, one 20-link piece, one 40-link piece, and one 10 piece.

To gain a better understandstanding, consider the scenario in the first few weeks as illustrated in the table below.

Weeks: Gold Links Given:
1 1
2 1 + 1
3 1 + 1 + 1
4 1 + 1 + 1 + 1
5 5
6 5 + 1
7 5 + 1 + 1
8 5 + 1 + 1 + 1
9 5 + 1 + 1 + 1 + 1
10 10
11 10 + 1
12 10 + 1


The table above indicates that:
at the end of the fifth week, the 5-link piece is given and the 4 one-link pieces are taken back;
at the end of the tenth week, the 10-link piece is given and the 4 one-link pieces as well as the 5-link piece are taken back.
 
Edit: 12 - 10 + 1 + 1
 

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