Minimum number of links he would need to cut?

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A wealthy merchant's son, left with a gold chain of 123 links, must pay weekly rent for his city apartment and shop using the chain. The rent structure requires him to pay one link after the first week, two links after the second week, and so forth, totaling 123 links over 123 weeks. To minimize the number of cuts needed to meet this payment schedule, he can strategically cut the chain into segments that allow him to pay the exact amounts required each week. The optimal solution involves cutting only four links, enabling him to make all necessary payments without exceeding the total number of links he has.
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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 123 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. If the son wished to rent the place for 123 weeks, what would be the minimum number of links he would need to cut?
 
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