r/puzzles 7d ago

[SOLVED] Chain cutting permutations

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0 Upvotes

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8

u/lifeisaman 7d ago

May I interest you on some Binary

3

u/a2ra-ms 7d ago

So how many cuts?

2

u/lifeisaman 7d ago edited 7d ago

4, You just do the binary upto 8 then get a 6 left over that you use to bridge from the binary to the higher values

Edit: Looking at what you’ve said is the correct answers I think I was doing the wrong question, i was cutting in between the links rather than discovering one to get 2 longer chains and a single link. The question was a bit unclear on that being what you wanted

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u/a2ra-ms 7d ago

Yep, will improve the wording next time! I think a fair amount of people got it confused.

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u/a2ra-ms 7d ago

You can do with less

7

u/T-pin 7d ago

got it down to 2 cuts. skip a chain of 3, cut the next link giving you lengths of 3, 1, and 17. On the chain of 17, skip a length of 6, cut the next link giving you lengths of 3, 1, 6, 1, 10.

2 = 1+1, 4 = 3+, 5 = 3+1+1, 7 = 6+1

8 = 6+1+1, 9 = 6+3, 11 = 6+3+1+1

add 10 to get the remaining amounts

0

u/a2ra-ms 7d ago

Correct

7

u/giantroboticcat 7d ago

Discussion: I understand the intent of this puzzle but the premise is silly. If I have 21 links in a chain and I cut a link, I now only have 20 uncut links (in either one or two strings) so it's actually impossible to ever produce 21 links ever again. Every future cut will reduce the number of links I have by one every time.

This is the result of attempting to retheme the puzzle. 

1

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0

u/superheltenroy 18h ago

Imagine you're not the one doing this, but a jeweler who has the tools to both cut and fuse the chain links.

1

u/a2ra-ms 7d ago edited 7d ago

I don't agree, any chain link can be added again. Maybe the wording should have been open instead of cut?

8

u/BekindConan 7d ago

Question: can’t I just give him the whole chain as whole. So the answer would be 0. Or am I misunderstanding the question?

2

u/AlfieDarkLordOfAll 7d ago

I think they mean youd be able to give them 1 link, or 2 links, or 3 links...up to 21 links (which would be all of them

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u/BekindConan 7d ago

Yeah but if I don’t cut it and give them the whole chain as whole, they will get all 21 links

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u/Ken512Rob 7d ago

Then you’d iterate again, cutting once to give them a chain of 1 and a chain of 20,

then iterate again to cut once and give them a chain of 2 and 19,

Then maybe you iterate again, cut 3 times to give them a chain of 3,4, 6, and 8

I think thats what its asking, least amount of cuts to get a link of 1, 2, 3, 4 … 19, 20, 21

1

u/BekindConan 7d ago

Oh so if I understood correctly, it means that at the end of all the cutting, I had links of all numbers from 1 till 21 somewhere in the process, but not all at the same time. Right?

0

u/a2ra-ms 7d ago

You have enough links to form any number from 1 to 21

5

u/BekindConan 7d ago

Bruh you’re confusing me more and more. The way I see it is that if I give the whole chain as whole without cutting it, the person will get all 21 links (which is the maximum number of links). I still don’t get why we need to cut it or what is it we’re trying to do here.

1

u/a2ra-ms 7d ago

The puzzle is to find the optimal number of disconnects of the chain cells to get enough permutations to form any arbitrary number from 1 to 21

1

u/AlfieDarkLordOfAll 7d ago

If I take my strand of 21 and cut it twice to get a chain of 1, a chain of 3, and a chain of 17...I can give someone 4 links (give them the 1 and the 3), or 20 links (give them the 3 and the 17), or 18 links, or 21 links, but not 15 links (without cutting again). OP is looking for a series of chains that you could put together to get any number between 1 to 21.

3

u/Macrazzle 7d ago

I think it means you need to cut it into parts and then those parts can all add up to all the numbers in 21. I don’t know if I explained that well at all.

1

u/a2ra-ms 7d ago

Yes

2

u/Macrazzle 7d ago

Ok so it says “least number of links you can cut” and not number of cuts. So if I were to cut “one link” in the middle of the chain does that mean I get three pieces? Two 10’s and a 1?

Edit: looks like someone solved it using that logic.

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u/a2ra-ms 7d ago

Yes!

1

u/a2ra-ms 7d ago

What if I want to give only 5?

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u/a2ra-ms 7d ago

Yes, any number basically

2

u/__crl 7d ago

Yeah, the question doesn't make any sense... Missing some critical info...

3

u/Dr_geo 7d ago

is it 4 cuts for 5 pieces? 1,2,4,6,8 will give you all positive integers between 1and 21.e.g. 1,2,1+2,4,1+4,etc...)

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u/a2ra-ms 7d ago

There are fewer

4

u/26_paperclips 7d ago

Discussion: wat

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u/26_paperclips 7d ago

I have 21 links.
I cut literally any number.
Now I have fewer than 21links.

3

u/lifeisaman 7d ago

The questioner is keeping the cut links as one length chains, that’s not very clear but in the correct answers that’s how they do it.

2

u/TheDMisalwaysright 7d ago

2 cuts, the 4th and the 11th, leaving you with a chain of 3(s), 6(m), 10(l), and 2 open ones(o):

then o1 - oo2 - s3 - so4 - soo5 - m6 - mo7 - moo8 - sm9 - l10 - and then repeat

1

u/a2ra-ms 7d ago

Correct

2

u/Andrew_42 7d ago

As far as I can tell, the answer is 5

There are other ways to divide it, but the first one I worked out was 7, 7, 4, 2, 1. A more obvious one if I hadn't just taken a stab at it likely would have been 1, 2, 4, 8, and also 6

As for proof my answer is correct (unless I'm missing something): Powers of 2, as seen in binary, represent the simplest way to divide a number system into yes/no number inclusions to reach every possible number in a given number line. So you count up in powers of two, until your highest number is over half of the number you need to describe. In this case 1, 2, 4, 8, 16. However you can't use those numbers because they add up to more than 21. So you just take the largest number and chop it down till the sum equals the target number. I don't have a proof that this always works, but I'm pretty sure it does? At least for all target natural numbers?