Logic Masters Deutschland e.V.

Standard sudoku rules applies. Fill the grid with numbers from 1 to 6 so each digit occurs exactly once in every row, column and 2x3 box.

A black dot indicates that the first two cells on one side of the dot have a difference that is double the difference of the first two cells on the opposite side.

A white dot indicates that the first two cells on one side of the dot have a difference that is 1 higher or lower than the difference of the first two cells on the opposite side.

The dot between the difference of 1 and 2 can be black or white.

All possible dots are given. Here is an illustration.

Here is the main course.

here’s a bonus. You’ll see.

A black dot indicates that the first two cells on one side of the dot have a product that is double the product of the first two cells on the opposite side.

A white dot indicates that the first two cells on one side of the dot have a product that is 1 higher or lower than the product of the first two cells on the opposite side.

The dot between the difference of 1 and 2 can be black or white.

All possible dots are given.

These puzzles are made by Old Miles from China. The reason why we didn’t create this back then is because it’s too hard and it’s kind of boring. that's why it’s a 4 star. I definitely don’t want to solve it again. I ask Old Miles to do this because I started to develop this portal’s idea at this idea. And what really disappoint me is that Richard said he didn’t found inspiration and PrimeWeasel called the his origin puzzle monster. I guess nobody tried to solve the 9X9 without given digit, which is what I originally tried to solve. And guess what, there is a 9X9 version of this difference kropki, which I just can’t solve. There’s just nothing to brute force with.

If you are wondering why there’s given digit in these three, I can tell you the reason. For the product, there’s only one combo for each dot. Each combo contain 4 digits, two of them are the same. So if there’s no given digits, switching the same digit and the other two in the combo would result in another solution. As for the difference kropki, the difference has no direction, so the end can be switched. Like 1 with 6, 2 with 4. because they and symmetrically the same. What did I learn? First, difference is always harder than sum with half the number range. Second, every difference rules need to have something to break the symmetric to create an empty grid. Third, two cell plus rules is hard in its nature. I’m not touching that at least for a long time.

BTW, I’m going to rip out RockyRoer’s median idea for a series of puzzles. For maximum entertainment, you probably should check his medium series, or his recent puzzles. I bet nobody is going to foresee what I’m going to post next. I can give you a hint, it’s only possible in 6X6, but it’s easy, because I made it.