Riddle: A traveler finds herself in town...?

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sshaina25

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A traveler finds herself in Town without funds; she expects a large check to arrive in a few weeks. Her most valuable possession is a gold chain having 23 links. To pay for a room, she promises to give the hotel as collateral one link a day for 23 days. She wants to damage the chain as little as possible. She can give the hotel a separate link each day, or she can give the hotel one link on day 1, then on day 2, take back the link and hand over a chain piece with two links. on day 3, she can give the single link again and on day 4, take back the links and give a chain piece with four links. All that mattes is that each day, she must be able to pay with the number of links corresponding the the number of days. What is the smallest number of links the traveler must cut off to meet her payment obligations for the full 23 days? you must tell which links should be cut.
 
I got links of 1,2,4,8, and 8.

As you can see each number is double the number before it, and the numbers before it add up to 1 less than the new number. The double 8 at the end is because there are only 8 links left on the chain. If you wanted to continue the process infinitely with an infinitly long chain, the length of each set of links would double.

Cool problem, thanks!
 
ok that is a very tough and confusing problem!(looking 4 paper but stopped) I will not answer it fully because i cant seem to find paper around these parts. I can just say by the last day she probably has 1 left over!
 
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