## Friday, February 10, 2012

### 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?

1. 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??