The puzzle below features each week in a TV guide. It's called "Number Workout" there but I've done a bit of research and it seems to be called "Hexanum" elsewhere. It bears some resemblance to Sudoku, in that it's a logic puzzle with a single solution.
Transcription: "Fit the numbers 1-6 once in every hexagon so that where the hexagons touch, the numbers are the same."
I've done lots of these and I have been able to solve them using simple techniques. In terms of the Sudoku ratings listed here, it would be "Level 1" techniques: choosing a number and seeing where it can fit in each hexagon. (Several times I have got stuck, but when I finally found a new number it was still by simple deduction.)
So my question is: Is it possible to construct one of these puzzles, with a unique solution, that requires more advanced techniques to solve? Note it doesn't need to be the same size as the one below - a smaller or larger puzzle may be required to prove it.