In 1492, what was the shortest distance you could travel to discover the new world from the old world?
score:6
0 meters, as the known world (that is, known by Europeans, which I assume you mean) already included parts of the "new world", ie Greenland and the coast of Canada.
As for the distance between the "old world" (ie Afro-Eurasia) and the "new world" (ie the Americas), the Bering Straight is about 80 kilometers wide. However, very few people live either side of it, so that's not much use. (Unless you include islands, in which case Iceland straddles the mid-Atlantic ridge, which means Reykjavik is in America, but that's really stretching "New World"...)
Other relevant distances:
The distance between Iceland and Greenland is as little as 300 kilometers, and Icelanders were completely aware of Greenland at this time, but there wasn't much reason to go there. The last Norse people on Greenland probably died quite shortly before Columbus travels.
The distance between Reykjavik and L'Anse aux Meadows, where there was a Norse settlement for a short time (probably just a winter) who were driven away by the native Americans, is about 2400 kilometers, which can be compared with the around 6900 kilometers Columbus traveled from Europe to land in America on his first voyage.
I assume your question really is about "Could there have been some other easier way to discover America", and the answer is yes. And in fact it had been discovered at least twice before. Once by the people who first moved there about 13.000 years ago, and secondly by Leifr Eiríksson around the year 1000.
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