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Brain Teaser #4?

  1. Jul 4, 2003 #1
    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......
     
  2. jcsd
  3. Jul 4, 2003 #2
    See, no one knows the answer becaue it's wrong!!
     
  4. Jul 4, 2003 #3
    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.
     
  5. Jul 4, 2003 #4
    Edit: 12 - 10 + 1 + 1
     
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