On Friday I posted this puzzle…

A woman arrives at a hotel. She has no money, but does have a gold chain containing 7 links (like the one in the photo, but gold). She does not know how long she is going to stay, but offers to give one link for each night she remains in the hotel. However, the links are tricky to saw and so the woman wants to make the smallest number of cuts possible .

The hotel owner is happy with this, and agrees to be helpful by exchanging links (so if, for example, the woman has given him three joined links in the past, she can pay for an extra night by giving him four joined links and he will give back the three joined links).

What is the smallest number of cuts that will allow the woman to pay night on night?

If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.

Night 4: Takes back all of the links and gives the 4 links
Night 5: Gives the single link
Night 6: Takes back the single link and gives the double
Night 7: Gives the single link

Did you solve it? Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for theKindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

1. david says:

My answer was 2 cuts for the same reason.

2. Goliath says:

Yes, got it. I will not call it too easy, otherwise I will not be able to solve any of Richard’s puzzles in months…

3. -M- says:

I thought it was 2 cuts at first. Later that day I figured 1 cut was enough.

I forgot to pack the hacksaw.

Richard

Your answer is perfectly fine if the question does not include the section:-

“so if, for example, the woman has given him three joined links in the past, she can pay for an extra night by giving him four joined links and he will give back the three joined links”

How could this scenario possibly happen if the woman had given the hotelier one link on one day 1, which is implied by “night on night”? Where has that one link gone to in this example?

An example does not have to be consistent with the “right” answer but it should be consistent with a possible answer.

TMT

1. -M- says:

It is possible: the cut link can be easilly put to the two links. It’s a “joined” 3-link chain then. And also: the example does not nessecarilly mean that that is the right way of cutting… It’s just an example.

2. Dormouse says:

You have a point. But does the wording of an example have to be consistent with the solution? You just said no. Does it have to be possible? Maybe not if it is just demoing the principle. But if it has to be possible, then you are right, if the word joined means never split up.

The section cant be reworded either, it could never be true according to the problem statement except for the hotel handing back one to get two joined on night 2. At night 3 or 4 or 5 or 6 or 7 the desk clerk is always handing back separated chains (0 back, 2 and 1 back, 0 back) except at 6 he is handing 1 back to get 2 and at 7 he is handing 0 back).

3. lindamp says:

No, a “for example” is merely to demonstrate what he means by “exchanging links”. If the example were part of the solution, then he’d be giving us the answer, which would immediately break the standing rule of “do NOT post your answers”.
For my part, I couldn’t see how the example could possibly be part of the answer as no way of cutting could possibly give you 3 joined AND 4 joined; all you could get is 1 + 3 + 3 or, as in the given solution, 1 + 2 + 4.

4. Anon says:

Agreed. Had RW said on night 27.36 she gives him a pomegranate and he gives her back a kangaroo it would have been about as consistent with the question and stated answer as the example he gave.

6. Dr Shaw says:

A VERY GOOD SPIN ON WORDS ANY THING IS POSSIBLE

7. Charles Sullivan says:

I’m with the Masked Twit. By that example, she could just give the entire seven-link chain to the hotelier on the first night, and when she leaves just cut off the balance owed her. One cut is all that’s needed.

8. Dormouse says:

I knew it! Two was too obvious. What is so invisible about the answer tho? Couldn’t see it. Why not? This is trickery, Sir. Somehow you hide the almost obvious behind the obvious.

Someone drank my tea while I was asleep…

9. One Eyed Jack says:

This is why they invented credit cards.

I neglected to pack a hacksaw. Schoolboy error.

11. Lazy T says:

it must be a very thick chain or a very poor hotel

12. Owen says:

Ah. I was thinking hand thr hotel owner all 7 links on thr first night and then when she checks out after however long days, the hotel owner makes a single cut to return any links which needed to be returned, say she stayed 5 nights then he would return 2…

13. Dharmaruci says:

i am puzzled but not in the good way. the puzzled problem states their is a three link section. but in the answer that has vanished,

1. lindamp says:

No, because she can’t give 2 links. Or 5. And the problem doesn’t state there has to be a 3 link section, see my comment above.

2. Dharmaruci says:

thank you for explaining. problem was misleading for me,

but she can give 2 links. Give three link while taking one link back. 3 -1 is two links for that night, eh?

3. No! Giving 3 links and getting 1 back means that she would be paying double the one-link-per-night rate for the seciond night, because by night 2 she qould have given 3 links and would have only 4 links left to pay for the final 5 nights.

4. Dharmaruci says:

thank you again. but i believe my earlier statement is correct. she is allowed to overpay provided all is settled on the final checkout, yes?

5. Anon says:

I think that night on night is meant to suggest that she has to pay every night and also pay the exact amount every night, Dharmaruci.

14. spiderabc1 says:

Embarrasingly enough my answer was zero. “What is the smallest number of cuts that will allow the woman to pay night on night?” Well it was agreed, she is allowed, so she doesn’t need to make a cut. Not until payment.

1. spiderabc1 says:

contd.. The first payment being made on the second day. I was thinking the reference to binary was because of the 0 and 1.

15. 3 cuts: links 2,4,6 need to be cut. Cut link 2 and remove link 1 on night 1; remove link 2 on night 2; repeat with 3/5 and 5/6 then you are left with link 7 for night 7. Why give 1 each night without getting ‘change’? Because the landlord is a tight-wad who banks each link on the day it is given!

Of course, given that in the example the landlord does give ‘change’, then cutting once (link 3) does indeed work, as with one cut, the links on either side (2 attached to 1 and 4 attached to 5,6,7) can be removed from 3.

Why does it work? Because once you have chains of length 1,2 and 4, you can create a simple binary sequence 1-7.

16. chivnick says:

Surely the act of cutting a link destroys that link? So one cut would leave just two, four and a bit of metal that used to be a link in a chain?

1. -M- says:

Yes, but it’s gold… I’d like to have that bit of metal.

2. No, it doesn’t. I’ve reused cut links when I’m making necklaces. You cut through the link on one end, then bend it back together. If you want it to be really secure, you can solder or melt it back together, too.

17. Jerry says:

A clever puzzle. I saw the 1,2,4 pattern right away, but did not see how to create it with only one cut. Very nice!

18. John says:

The answer I got in about 20 seconds was the correct one.

1. Dormouse says:

20 seconds, and I failed in three days? Did you go to university at age three, or are you just good at doing puzzles? Please contact the White House to help with Afghanistan.

19. Indigo May Roe says:

I got it before I finished reading the question.

1. Nanny Mouse says:

I got it before I was born

2. Bumfluff says:

I got it before the creation of the world

3. Dave says:

The answer to next week’s puzzle is 7 inches long

20. Wigan FC says:

I got it before the big bang

1. Photon Boy says:

I got it in a parallel universe

21. Photon Boy 2 says:

I got it in a parallel universe

1. Dave's mate says:

Oi, no spoilers please, I’m still working on this

22. Why are a tiny minority of mad people whingeing and moaning and complaining about the wording of the bit which says “for example…”? Don’t people know what “for example” means? The correct answer as given above was immediately obvious to anybody who has ever known anything about binary.

1. Richard's Dorkings says:

They are just a bunch of nutters who are only able to read the question properly.
Ignore them John.

23. Yep, that was the answer I eventually came to whilst writing down how quickly I’d got the answer that turned out to be wrong.

24. rimbaud3000 says:

I have reincarnated endlessly since the beginning of time. I have carried the answer to this question in the energetic matrix of my being for the sole (soul?) purpose of writing this post. My task should be soon complete.
Unfortunately, I got a little distracted during the dark ages. It got messy, believe you me.
So I forgot. Meh, who doesn’t forget things sometimes?
I thought to myself (for the past thousand years or so) “Two cuts, two cuts, don’t forget!”
Two cuts. Oh well, never mind. There will be other universes, other tasks.
One bloody cut. Was that so hard to remember?
What a waste of time.
Now I am just a little upset about it actually.
I mean, dinosaurs, protozoa, mass extinction events, surviving as a whisp of plasma in the first nebulae, THOSE I can handle, but a bit of bubonic plague and four hundred years of religious oppression and I go to pieces.
I might even swear.

25. Nigel says:

Yup, took me about 10 secs.