In the following grid, the numbers from 1 to 6 occur only once per row, per column, or per colored rectangle. Given the relations between numbers and a single number to get you started, can you complete the grid?

| | | | | | | | | | | | | |

| | > | | > | | | | < | | < | | | |

| v | | ^ | | v | | ^ | | ^ | | ^ | | |

| | < | | > | | | | > | | < | | | |

| | | | | | | | | | | | | |

| | < | | > | | | | < | | > | 3 | | |

| v | | v | | ^ | | ^ | | v | | ^ | | |

| | > | | < | | | | > | | < | | | |

| | | | | | | | | | | | | |

| | < | | < | | | | < | | > | | | |

| ^ | | v | | ^ | | v | | v | | ^ | | |

| | > | | < | | | | < | | > | | | |

| | | | | | | | | | | | | |

(In reply to

Excellent puzzle by Josie Faulkner)

Hey, thanks to you and to everybody that liked this! I liked the explained solution; it's nothing like the way I solved this!

I read about the idea of giving "relations" in sudoku diagrams, and decided to try for myself. My first experiment was a 4x4, but that was too easy. Since I didn't want to start with a 9x9, I opted for the 6x6. I managed to produce a grid in a short time, and started thinking about how many clues to give.

At first I gave no numbers at all (I thought that might be enough; after all, several numbers looked "obvious" such as the 6 in the purple rectangle) but on solving it, I found two solutions: in the white and purple rectangles, you could exchange the "2" and the "3", and still get a valid solution, so I had to fix one of those four cells.

I'm gearing up to do a 9x9 now...