Slalom is a puzzle originally from nikoli; you can see their description of the puzzle here. (Their name is “Suraromu”, but Slalom is much more descriptive; I don’t remember where I saw this name.*) The object is to draw a single closed loop through adjacent grid squares, with no square visited twice. The loop must pass straight through each gray line exactly once; if the line spans multiple cells only one of them should be crossed. The loop is considered to start from the circled number, which tells how many gray lines there are. If a gray line has a number written somewhere on it, that’s when it should be crossed. For example, a gray line with a 1 (if there is one) should be crossed first starting from the circle. The solution is unique.
Below is an example puzzle and its only solution.
* Reader Alan Curry pointed out to me that “Suraromu” is an Engrish way of saying “Slalom” with the typical l/r switching and throwing in of vowel sounds. I feel a little dumb for not spotting that one. Thanks for mentioning that.