The History of Link Puzzles
Joining pairs with lines that may not cross is an old puzzle idea - Sam Loyd printed a form of it in 1897.
Early Versions
In 1897 a slightly different form of this puzzle appeared in a newspaper column by Sam Loyd in the Brooklyn Daily Eagle. In 1917 Henry Ernest Dudeney included a version with pairs of letters in his book Amusements in Mathematics, as a puzzle for motorists.
Numbers and Letters
In Japan the puzzle publisher Nikoli made the puzzle popular in two forms: with pairs of letters and with pairs of numbers. The general name of the puzzle is Numberlink. A puzzle counts as well made when it has exactly one solution and the lines fill every cell.
How PaperGames Makes Each Puzzle
The puzzles here were made in advance by PaperGames's own generator: it lays random lines that together run through every cell, then a solver checks that there is exactly one way to join the pairs. Where it finds a second way, a line is split into two pairs; lines whose ends touch are joined again as long as the solution stays the only one.