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Question 85828: please sir,help me to solve this question fast and urgently.
the question is - mala has a beautiful necklace,made up of 5 sections,each section consisting of 4 links.once she took the necklace to a goldsmith and asked to give her an estimate to join the 5 sections into one piece necklace.the goldsmith demanded Rs 2 to cut open a link and Rs 2 to solder it together again.what is the cheapest method to get these 5 pieces joined together in one full necklace? how much would it cost?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The problem describes Mala's necklace as being 5 sections of 4 links each which can be
represented like this:
.
oooo oooo oooo oooo oooo
.
Normally you would think that you link them by opening a link at the end of one of the sections,
linking it to the next section and closing the link to join the two sections together.
This means that you would cut a link for each of the open spaces shown above and solder it
back together to make the necklace a single piece. Since there are 5 open spaces to
be linked as shown above (the 4 spaces in the string plus the end needs to be joined to
the beginning), this would require 5 links to be cut (one link at the end of each section)
and resoldered which would cost Rs 10 for unsoldering 5 links and Rs 10 to resolder the
5 links, a total of Rs 20.
.
However, what if the goldsmith took one of the sections (4 links) and cut each of the
links open in that section? Then Mayla would have a necklace consisting of the remaining
4 sections and 4 open links as represented below:
.
oooo oooo oooo oooo o o o o
.
The 4 spaced links shown above represent the one section in which each link has
been opened.
Notice now that there are 4 sections to be joined, so there are 4 links to
be made
(three spaces shown above plus linking the end to the start of the first section).
The goldsmith has 4 open links to make those 4 connections, so he just links the 4 sections
with the 4 open links and resolders them. This means that the goldsmith gets Rs 8 to open
the 4 links and Rs 8 to resolder them in linking the 4 remaining sections of the necklace ...
a total cost of Rs 16.
.
This appears to be the cheapest way of having the one-piece necklace made.
.
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