At least this time I might actually be addressing multiple readers.
For the number 3, Double Back instantly sprang to mind. I had already done it with different numbers in my Four Colour Loop puzzle. I'm not the first to do Triple Back, as it has appeared on Palmer Mebane's blog as well. I like how this one turned out. I think once you get started with this puzzle, it shouldn't cause too many problems.
3. Double Back; Triple Back
Draw a single closed loop through all cells in the grid. The loop must pass through each boldly marked region exactly thrice.