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Math Help - A Problem Solving Question

  1. #1
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    A Problem Solving Question

    In one of his journeys, Gulliver walked into a castle. The king, who was the owner of the nastle, greeted the famous traveller with all honours and invited him to share his evening meal. After the meal the king asked Gulliver about his adventures andw as particularly interested in the golden chain that Gulliver found on his last journey. The king was so attracted to the chain that he offered Gulliver a deal: the next morning the king would ask Gulliver to sell him and unspecified number of links of the chain for a very generous price, if Gulliver managed to give the king exactly the requested number of links, he would get the money and freedom; otherwise he would lose the whole chain and stay with the king forever as the Royal Storyteller

    Of course, the king took all care to ensure that there were no cutting or sawing tools in the bedrrom where Gulliver had to spend the night. But the experienced traveller remembered that he had a nail-file. He knew he would need the whole night to cut through one link. Then he realised that by cutting one link wisely he would be able to give the king the exact number of links regardless of how many the king would request, and started to work. (Gulliver knew that the cut link would be considered as an ordinary link.)

    At the end of the night, when he got very tired, he discovered that if his chain contained more links, in order to be sure that he could het freedom (and money), he would need to cut at least two links. This interesting thought gave Gulliver the energy he needed and he quickly finisheh the job. Soon he gave the stunned king the number of links the latter asked for, and left the castle with a carraige full of money. How many links were in Gulliver's chain?

    any help would be great
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  2. #2
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    hey

    the answers 7 links in the chain.
    all number of links work until the 8th one.

    i cant reeli be bothered to draw it but, if u cut the chain at the first and3rd interval then u can get any number of links required

    ie: cut it like this: the gaps are the cuts-->0 00 0000
    then u get 1,2....up till 7

    soz im crap at explaining buh i hop it helps

    i didnt reeli read the q --i dun noe how many cuts --sorri

    hope it helps neway
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  3. #3
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    Hello, Chuck!

    This is a classic (old) problem.
    . . phatjigga had the right approach, but he/she cut two links.


    There were indeed seven links in the chain.

    Gulliver cut the third link.

    With sub-chains of: oo\quad o\quad oooo
    . . he could provide a set of 1, 2, 3, 4, 5, 6, or 7 links.

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

    There is a similar problem that may amuse you . . . or not.

    A woman has five gold chains with four links each.
    . . oooo\quad oooo\quad oooo \quad oooo\quad oooo

    She wanted them connected in a circle to make necklace.

    It costs $1 to open a link and $1 to close a link.

    What is the least she must pay to have the necklace made?

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