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?

Guest Aug 23, 2019

#2**+1 **

In a row, I break and weld the second and fourth segments.

This costs \(2\times (5\ Cents+10\ cents)=30\ cents\)

!

asinus Aug 24, 2019

#3**0 **

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.

Melody Aug 24, 2019

#4**+1 **

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

O O O O O

\(\uparrow\) \(\uparrow\)

!

asinus Aug 24, 2019

#6**+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**+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.

Rom Aug 24, 2019