In one of his journeys, Gulliver walked into a castle. The king, who was the owner of the nastle, greeted the famous traveller with all honours and invited him to share his evening meal. After the meal the king asked Gulliver about his adventures andw as particularly interested in the golden chain that Gulliver found on his last journey. The king was so attracted to the chain that he offered Gulliver a deal: the next morning the king would ask Gulliver to sell him and unspecified number of links of the chain for a very generous price, if Gulliver managed to give the king exactly the requested number of links, he would get the money and freedom; otherwise he would lose the whole chain and stay with the king forever as the Royal Storyteller
Of course, the king took all care to ensure that there were no cutting or sawing tools in the bedrrom where Gulliver had to spend the night. But the experienced traveller remembered that he had a nail-file. He knew he would need the whole night to cut through one link. Then he realised that by cutting one link wisely he would be able to give the king the exact number of links regardless of how many the king would request, and started to work. (Gulliver knew that the cut link would be considered as an ordinary link.)
At the end of the night, when he got very tired, he discovered that if his chain contained more links, in order to be sure that he could het freedom (and money), he would need to cut at least two links. This interesting thought gave Gulliver the energy he needed and he quickly finisheh the job. Soon he gave the stunned king the number of links the latter asked for, and left the castle with a carraige full of money. How many links were in Gulliver's chain?
any help would be great