# So I have a problem...

You have four small chains with three links each. You want to combine the four small chains into one necklace you can wear around your neck. It costs you ten cents to break a link of chain, and 20 cents to weld it together. What is the least expensive price you can pay to create a necklace of 12 links around?

Someone can explain it to me? Thanks.

Note by Half Pass3
8 months, 3 weeks ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

90 cents I think. You can take one of the chains, break all its 3 links, then use them to join the rest into one necklace. This gives us 3 breaks and 3 welds, which amounts to 90 cents.

- 8 months, 3 weeks ago

I have to state, 10 cents to break a LINK instead of a whole chain. and to make all 12 pieces into a circle.

- 8 months, 2 weeks ago

So is my answer correct @Half pass3?

- 8 months, 2 weeks ago

Not a same problem but See Here. That last line there should've been here.

- 8 months, 2 weeks ago

See the solution is same as mine.

- 8 months, 2 weeks ago

- 8 months, 2 weeks ago

@Devbrat Dandotiya sorry to tell you, but I checked and @Percy Jackson 's answer was correct.

- 8 months, 2 weeks ago

If by links you mean the rings themselves, then there are 12 rings in total already, hence you can only weld, which will be four times for four chains, or 20×4=80 cents.

If by links you mean the connections between the rings, then there are 16 rings in total. Here three chains would be enough to make a 12 rings necklace and 3 welds are the only requirement, or 2×30=60 cents.

- 8 months, 3 weeks ago

Don't forget that you have to break a link before welding it to join two chains, so both your answers are wrong @Devbrat Dandotiya

- 8 months, 3 weeks ago

Don't forget that that is already the reason why welding is more expensive

- 8 months, 3 weeks ago

Thanks for helping me out so much.

- 8 months, 3 weeks ago

Nope, that hasn't been mentioned. Practically even, breaking a link is much is easier than welding it, so welding is costlier. If it is so, then @Half pass3 hasn't stated his problem very well, and has left the solvers to guess out the specifics. If that is not the case, then I am simply correct, and you aren't @Devbrat Dandotiya :)

- 8 months, 2 weeks ago

Even if the problem isn't stated very well @Percy Jackson my solution makes less assumptions than yours.

- 8 months, 2 weeks ago

Actually, your solution makes the impractical assumptions that would simplify this problem. I took the practical assumption in my problem. You might as well have said that you could do it in 0 cents because a magic fairy helped you. In chain links, you always break and then weld, and welding usually costs more as it requires more work and precision than breaking a link.

- 8 months, 2 weeks ago

If I want to 'simplify' this problem which has already no specifications then I'm just being rational and hence it's not just about making 'impractical' or 'practical' assumptions but about making none or some.

- 8 months, 2 weeks ago

You are not making sense, as you are stating the same argument using different words again and again. Silence is the best answer to those who don't value your words, so I'm putting a pin on this conversation, and ending it. No use explaining it to people who don't accept they are wrong...........

- 8 months, 2 weeks ago

I might have agreed with you on the fact that the problem is poorly stated, but my reason of argument is that you've in the first reply claimed that my answers are wrong, as if you know what the question really should have been. If only by bringing the argument of 'assumptions' again and again I've become nonsensical, then where do you stand @Percy Jackson with your repeated argument of 'practicality'?

- 8 months, 2 weeks ago

My argument of 'practicality', is that when problems don't have specific information in them, you cannot make any assumptions. You will have to use real life information. You can't round off g to 10 if the value of gravitational acceleration constant isn't given. You'll have to use 9.81 m/s^2, so in the same way, you can't assume that welding is costlier as it is inclusive of breaking. Anyway, even if you reply to this comment, I will not reply, let's leave the topic.

- 8 months, 2 weeks ago

I have not assumed that welding is costlier as it includes breaking, I only tried to explain the obscurity in the problem by not assuming that it does not include breaking.

- 8 months, 2 weeks ago

But then at last I have to agree on that you might have been right all along which I kind of knew, I mean, why else the price of breaking would even be there when my solution doesn't even need that. It being there shows that breaking matters and that the price of welding is exclusive.

- 8 months, 2 weeks ago

I have to state, 10 cents to break a LINK instead of a whole chain. and to make all 12 pieces into a circle.

- 8 months, 2 weeks ago

And 'magic fairies' are just an strawman argument.

- 8 months, 2 weeks ago

Well, you're being a strawman here :)

- 8 months, 2 weeks ago

Sure

- 8 months, 2 weeks ago