Discovered Angles
(Eingestellt Gestern, 12:06 Uhr von Grumpy)
I was inspired by meggen033's GAS puzzles and thought I'd create my own variant of it. It's maybe not as smooth, but hopefully still enjoyable :)
This is only my second time setting a Sudoku, and I think it's a vast improvement on my first. But I am definitely not an expert, so I'd love to hear your critiques in the comments!
Rules
- Normal Sudoku rules apply.
- Killer Cages: Digits in cages sum to the number in the top left of the cage.
- Kropki Dots: Cells separated by a black dot have digits with a ratio of 1:2. Cells separated by a white dot are consecutive. Not all dots are given.
- V Sums: Cells separated by a V sum to 5. Not all V Sums are given.
- Angle Sums: Green angle sum cells have an angle in the top left, and a sum in the bottom right. Draw a line from an orthogonally connected puzzle bound to the Angle Sum cell, then rotate the input line (cw or ccw) by the angle in the top left, and continue to draw a line until you hit another puzzle bound. Digits along this line must sum to the number in the bottom right. There is only one correct rotation. Lines may overlap. A line may only count the digit in its own angle sum cell once. Lines must have a length of at least 1, not including the Angle Sum cell itself
For more information about how angle sum cells work, scroll down further.
Play on SudokuPad!
Further explanation of Angle Sum rule
Consider Figure 1 in the graph below. R2C3, R2C4, and R4C3, R4C4 cannot be disambiguated without the Angle Sum constraint. The rotation of the Angle Sum cell is 45 degrees, and the sum must be 13. In Figure 2, we attempt to start from the left bound of the puzzle, but no matter if we rotate clockwise or counterclockwise, we cannot get to the sum of 13 if we add up the digits. This is therefore not the correct angle.
We try the same thing, this time from the top, in Figure 3. Here, there is a way of accumulating a sum of 13, but only if R2C3 is 3. Checking from the right bound and bottom bound, we can see that the green arrow in Figure 3 is actually the only way we can get to the sum of 13. Therefore, R2C3 must be 3. The puzzle can now be completed.
Lösungscode: Row 9
Kommentare
Gestern, 22:17 Uhr von Grumpy
Added clarifying rule about minimum line length.
Gestern, 19:57 Uhr von Grumpy
@Marshal on Mars
That is possible, yes. Though that cannot happen in this particular puzzle. I'm not sure it's worth specifying in the rules, because it could always just be deduced... I think.
---
@Iluvsodah
Hm, that could work. The "one line has to be horizontal/vertical" still makes it a bit awkward to me, but I think there's something to your suggestion, for sure.
Gestern, 17:20 Uhr von Marshal on Mars
Can the line that enters the angle-sum-clue cell originate from a border of the grid that is also a border of that cell?
For example, for an imaginary grid, if r1c1 contained an angle sum clue, could the line entering it enter from r"0"c1?
Is that something we should know about how the constraint works, or is that left to be deduced?
Gestern, 16:33 Uhr von Iluvsodah
My two cents on the angle rule. I would invert the 45 and 135 degrees, and state the rule like this :
- Project two lines from the digit in an angle cell.
- At least one of the lines needs to be horizontal/vertical
- The two lines are separated by the angle stated in the cell
- The sum of the digits on the lines (counting the angle cell itself once only) sum to the sum in the angle cell
Gestern, 14:54 Uhr von Grumpy
If anyone has suggestions on how to phrase the constraint/rule more effectively, please let me know. It's very clumsy right now, which makes it seem much more complicated than I believe it is.
Gestern, 14:14 Uhr von Grumpy
Added further explanation of the Angle Sum constraint, with an example.
Gestern, 13:57 Uhr von StefanSch
The angle sum rule is hard to understand. An example would be nice.
