|Subject:||the nine dots|
The way your "dots" are drawn (on the hint page, https://www.cut-the-knot.com/ghint.shtml), and indeed they always are drawn when this problem is given, it is possible to use only three lines. Sufficiently long and almost parallell to each other, they will touch 3 dots each (although not in the center, but who said they had to?). I have not invented this solution myself, and you may think it is silly, but I think it is ingenious. I saw it in a book about children's inventiveness when given different problems and "free hands" to solve them. Indeed one child suggested a way to do it with only one or two lines. I do not remember how, but it involved folding the paper with the dots (will not work on a screen!).
Lars Hellvig, Stockholm, Sweden