A five star hotel

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finallyskeptic
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A five star hotel

Postby finallyskeptic » Tue Oct 27, 2009 10:17 am

Sheldon is in a five-star hotel.He finds that he has no money left.He has a 63 link gold chain.
He has to live in the hotel for 63 days.
He has to give one link to the hotel staff everyday.
What is the minimum number of cuts required(for getting links from the chain) so that Sheldon lives in the hotel for 63 days with respect? :banghead:
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Re: A five star hotel

Postby vanderpoel » Tue Oct 27, 2009 11:28 am

Minimum one, but respect?
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Re: A five star hotel

Postby finallyskeptic » Tue Oct 27, 2009 3:08 pm

vanderpoel wrote:Minimum one, but respect?


Respect is just an add on.
One isn't the answer.
Spoiler:
He can even return links.
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Re: A five star hotel

Postby Gord » Wed Oct 28, 2009 4:25 am

Hmm, lemme try this. :write:

It's a Binary question. He'll need lengths of one, two, four, eight, sixteen and 32 links.

He starts with a 63-link chain. I'll represent links with the letter o, cut-links with the letter c, and joined links will be sequencial like this: ooo....

If he cuts the second link, he'll have one link and one cut-link:

o c ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

If he then cuts the third link, he'll have one link, two linked, and two cut-links.

o c oo c oooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

If he next cuts the ninth link, he'll have: One link, two linked, eight linked, and three cut-links.

o c oo c oooooooo c ooooooooooooooooooooooooooooooooooooooooooooooooo

If next he cuts the seventeenth link, he'll have: One link, two linked, eight link, sixteen linked, 32 linked, and four cut-links (which will serve as the four linked.

o c oo c oooooooo c oooooooooooooooo c oooooooooooooooooooooooooooooooo

Total cuts: Four. :mrgreen:

As for the sequence by which he pays:

  • On the first day, he pays one link.
  • On the second, he pays the two-link and is handed back the single link as change.
  • On the third day, he pays the single link.
  • On the fourth, fifth, sixth and seventh days, he can pay one cut-link each time.
  • On the eight day, he pays with the eight-link, receiving in change all the links he previously paid.
  • On the ninth day, he pays one link.
  • On the tenth, he pays the two-link and is handed back the single link as change.
  • On the eleventh day, he pays the single link.
  • On the twelfth, thirteenth, fourteenth and fifteenth days, he can pay one cut-link each time.
  • On the sixteenth day, he pays with the sixteen-link, receiving in change all the links he previously paid.
  • On the seventeenth day, he pays one link.
  • On the eighteenth day, he pays the two-link and is handed back the single link as change.
  • On the nineteenth day, he pays the single link.
  • On the 20th, 21st, 22nd and 23rd days, he can pay one cut-link each time.
  • On the 24th day, he pays with the eight-link, receiving in change all the links he previously paid except for the sixteen-link.
  • On the 25th day, he pays one link.
  • On the 26th day, he pays the two-link and is handed back the single link as change.
  • On the 27th day, he pays the single link.
  • On the 28th, 29th, 30th and 31st days, he can pay one cut-link each time.
  • On the 32nd day, he pays with the 32-link chain, receiving in change all the links he previously paid.
  • On the 33rd day, he pays one link.
  • On the 34th day, he pays the two-link and is handed back the single link as change.
  • On the 35th day, he pays the single link.
  • On the 36th, 37th, 38th and 39th days, he can pay one cut-link each time.
  • On the 40th day, he pays with the eight-link, receiving in change all the links he previously paid except for the 32-link.
  • On the 41st day, he pays one link.
  • On the 42nd day, he pays the two-link and is handed back the single link as change.
    On the 43rd day, he pays the single link.
  • On the 44th, 45th, 46th and 47th days, he can pay one cut-link each time.
  • On the 48th day, he pays with the sixteen-link, receiving in change all the links he previously paid except for the 32-link.
  • On the 49th day, he pays one link.
  • On the 50th day, he pays the two-link and is handed back the single link as change.
  • On the 51st day, he pays the single link.
  • On the 52nd, 53rd, 54th and 55th days, he can pay one cut-link each time.
  • On the 56th day, he pays with the eight-link, receiving in change all the links he previously paid except for the sixteen-link and the 32-link.
  • On the 57th day, he pays one link.
  • On the 58th day, he pays the two-link and is handed back the single link as change.
  • On the 59th day, he pays the single link.
  • On the 60th, 61st, 62nd and 63rd days, he can pay one cut-link each time.

Total: 63 days, one link at a time. :mrgreen:
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Re: A five star hotel

Postby Aztexan » Wed Oct 28, 2009 4:30 am

Five-star hotels only take cash or credit card. Sheldon would be out on his ass.
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Re: A five star hotel

Postby OlegTheBatty » Wed Oct 28, 2009 4:55 am

ruben lopez wrote:Five-star hotels only take cash or credit card. Sheldon would be out on his ass.


There's always pawnshops.... but then he would only have enough rings for a few days
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Re: A five star hotel

Postby scientia » Fri Jun 09, 2017 10:11 pm

Gord wrote:He'll need lengths of one, two, four, eight, sixteen and 32 links.
Total cuts: Four.

That's very clever. Let's see.
4--8--16--32
32+16+8+4 = 60 + the three cut links = 63.

Three cuts.

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Re: A five star hotel

Postby Gord » Fri Jun 09, 2017 11:02 pm

:mrgreen: You win.
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