Assignment:
A traveler owing a gold chain with 7 links is accepted at an inn on condition that he pay one link of the chain for each day he stays. If the traveler is to pay daily and may be given links already used in payment as change, show that he only needs to take out one of the links of the chain in order to pay each day for 7 days. (note: if he takes out the nth link he has 3 pieces of lengths i-1,1,7-i.)
Can you generalize this to n links? - how many links does he need to take out to pay for n days ?
Provide complete and step by step solution for the question and show calculations and use formulas.