Golden Chain Puzzle
The son of a rich bullion merchant left home on the death of his father. All he had with him was a gold chain that consisted of 148 links.
He rented a place in the city center with a shop at the lower level and an apartment at the upper level. He was required to pay every week one link of the gold chain as rent for the place. The landlady told him that she wanted one link of the gold chain at the end of one week, two gold links at the end of two weeks, three gold links at the end of three weeks and so on.
The son realized that he had to cut the links of the gold chain to pay the weekly rent.
Also consider that when any chain is broken to get links, three links are obtained, two partitions and one link from which chain was broken.
If the son wished to rent the place for 148 weeks, what would be the minimum number of links he would need to cut?
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4
5
upto 7 weeks, he need to break 1 link
upto 16 weeks he needs to break 2 links
upto 33 weeks he needs to break 3 links
upto 67 weeks he needs to break 4 links
upto 135 weeks he needs to break 5 links
upto 271 weeks he needs to break 6 links
Please confirm if it is right??
Break the following links:
#6, #17, #38, #79
You’ll have chain links of length 5, 10, 20, 40, and 69, as well as 4 individual links. You can combine any of these into any number from 1 to 148. For example, to pay on the 96th day, you retrieve all links already paid and give your landlord the 69, 20, 5, 1 and 1 link lengths. On the 99th day, take back all the single links and give him the 5.
Only 4 links need to be broken.
Edit: Incidentally, I believe this will work for a chain with up to 159 links (last link will have 80)