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You have 5 segments of a chain and you want to connect them together into one chain. It costs 5 cents to break a link, and 10 cents to weld it back together. What is the least it would cost to join the 5 segments together?

 Aug 23, 2019
 #1
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Oops, sorry I posted twice. My bad!

 Aug 24, 2019
 #2
avatar+8643 
+1

 

In a row, I break and weld the second and fourth segments.
This costs \(2\times (5\ Cents+10\ cents)=30\ cents\)

laugh  !

 Aug 24, 2019
 #3
avatar+105464 
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I am confused by your logic asinus.

I think it will cost 60cents   (4 connections needed.)

I am assuming that when you break a link you can then use it to join to another section.

 Aug 24, 2019
 #4
avatar+8643 
+1

I break a chain link and connect three chain links with it Melody.

O O O O O

    \(\uparrow\)     \(\uparrow\)

 

laugh  !

 Aug 24, 2019
 #5
avatar+105464 
+1

So you do not end up with one long chain? 

That is what I took the question to mean.

 

I still don't get what you mean.

 

You have 5 peices of chain so you need 4 connectors to join them into one long chain.

Melody  Aug 24, 2019
edited by Melody  Aug 24, 2019
 #6
avatar+105464 
+2

 

 

HERE ARE THE FIVE CHAINS

 

XXXXXX    XXXXXX     XXXXXX     XXXXX       XXXXX

 

I need to break 4 end links and use them to join the pieces back up

 

XX  X  XXXXXX   X  XXXXXX  X   XXXXX   X    XXXXX            15*4=60c

 

 

Of course if one small chain has less than 4 links then less joins will be needed.

 

 

If the shortest one is only 3 links then

XXX    XXXXXX     XXXXXX     XXXXX       XXXXX

becomes

  XXXXXX   X  XXXXXX  X   XXXXX   X    XXXXX            15*3=45c

 

 

 

If the two shortest ones have 2 links each then

XX    XX     XXXXXX     XXXXX       XXXXX

becomes

X   X  XXXXXX  X   XXXXX   X    XXXXX            15*3=45c      still 45cents

Melody  Aug 24, 2019
 #7
avatar+6045 
+1

The question is poorly worded.

 

Is the end result a single piece of chain in which all but the first and last link are joined to only two other links,

and the first and last link joined to only one other link, or not?

 

If not.  Break one link, attach all the pieces of chain at that link and reweld it.  Fifteen cents.

 

If so, Melody's solution above is correct.

 Aug 24, 2019

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