Fill a square grid with digits from 1 to its size, so that no digit appears twice in a row or column and every clue is satisfied.
A clue sits where four squares meet, and speaks of their two diagonal pairs:
On a touch screen, a tap does what a click does, and a long press what a right-click does (more ways to right-click). A key the puzzle’s controls show as a button can be pressed there instead of on a keyboard.
Left-click to select a cell, then type a number on your keyboard to enter it. Press Backspace, Space or 0 to clear a cell.
Right-click a cell, then type a number to add a pencil mark. Pencil marks can be used for any purpose. Pencil mode is sticky: once a right-click switches it on, it stays on wherever you click, until you right-click again. The Marks key is lit while it is on, and pressing the key also switches it. To have it last only until your next click, turn off Right-click toggles a sticky pencil mode (stays on until right-clicked again) in the preferences.
You can also use the arrow keys to move the selected cell around. Press Enter to toggle between entering numbers and entering pencil marks.
Press Fill marks among the puzzle’s controls to write in every pencil mark wherever nothing is placed and no mark is written yet. The M key does the same, on any board where M is not something you type. Marks you have narrowed are left alone, and pressing again never starts over: see Filling in all the pencil marks. Once every empty cell has marks, the press crosses out of each the numbers already placed in its row and column.
The inventor of Mathrax is unknown.
More information: https://www.janko.at/Raetsel/Mathrax/index.htm
Hint explains the next step rather than simply making it. It works from your own numbers and pencil marks, so it carries on from wherever you are; if a number you’ve entered is wrong, or a cell’s pencil marks have crossed out its answer, it asks you to fix the highlighted mistakes first. It pencils in only as it needs to: a cell with no marks counts as holding every number its row and column don’t already hold, and the hint writes a cell’s marks only when its next step crosses one out or reasons from them. If you would rather it filled in every cell’s marks first (the same as pressing Fill marks), set Hints pencil in to Every candidate first in the preferences.
The hint names a clue as it is drawn (“the 7+ clue”, “the 2÷ clue”, “the = clue”), and “the 3 across it” is the number in the cell diagonally opposite across that clue. A number is open in a cell while it is still possible there: in the cell’s pencil marks, or, in a cell with no marks, not yet ruled out by its row and column. So “nothing open across the 7+ clue adds with 1 to make 7” means the cell across can’t be 6, so this cell can’t be 1.
On the hardest boards that need no guessing, a step may be a wing. Take a cell whose pencil marks are down to two values, say a or b, and two cells it can’t repeat a value with, both outlined: one marked a and c, the other b and c. Whatever goes in the middle cell, one of the outlined cells must have c, so a cell that can’t repeat a value with either of them can’t be c. If the middle cell could be c as well, the same holds for a cell that can’t repeat a value with the middle cell either.
If you’ve turned on the preference that removes a number from pencil marks in its row and column when you place it, the hint leaves that tidying to the placement rather than spelling it out as a step of its own. On an Unreasonable board, deduction can run out before the grid is full; the hint says so rather than guessing.
These parameters are available from the ‘Custom type…’ option on the ‘Type’ menu.