Rules
Slant is a diagonal puzzle. Every cell gets one diagonal, from corner to corner. A backslash runs from the top-left corner of the cell to the bottom-right. A slash runs from the top-right corner to the bottom-left. Numbers sit on the points where the grid lines meet, inside small white circles. The number is how many diagonals touch that point. A point with no circle does not constrain the count. A corner has one cell, so its number is 0 or 1. A point on the edge has two cells, so its number is 0, 1, or 2. A point inside has four cells, so its number is 1, 2, 3, or 4. The diagonals may branch, and they may stop. They must not close a loop. A loop is a cycle that returns to a point it has already left. While you play, a number that can still be met stays quiet. A clash is a number that already has too many diagonals, a number that cannot be reached even if every empty cell around it is filled, or a diagonal that already sits on a closed loop. The puzzle is finished when every cell has a diagonal, those diagonals match the one solution, and no clash remains. Play and print are 5×5, 6×6, 7×7, 8×8, 9×9, 10×10, 8×6, and 10×8, each at easy and medium. The 8×6 board is 8 rows by 6 columns. The 10×8 board is 10 rows by 8 columns. The daily puzzle is a 7×7 easy grid. People also look this up as a slant puzzle.
- A clue. A number in a white circle sits on a grid point. It is how many diagonals touch that point. A point with no circle does not constrain the count.
- A diagonal. Every cell gets one, from corner to corner. A backslash runs from the top-left corner to the bottom-right. A slash runs from the top-right corner to the bottom-left.
- A clash. A number that already has too many diagonals, a number that cannot be reached even if every empty cell around it is filled, or a diagonal that already sits on a closed loop.
The picture of a finished grid draws the solved diagonals in teal. The frame stays ink. The circles stay white. The numerals stay ink. No yellow. No ring. A printed puzzle page shows the grid and the numbered circles, with no diagonals. A printed answer draws each diagonal as a thick line under the circles. On screen, that answer matches the print. The PDF is black and white.
- Clue
- Diagonal
- Clash
Tap a cell to cycle empty, then a backslash, then a slash, then empty again. Right-click, or press and hold, cycles the other way. After the first tap, drag across cells to paint the diagonal that tap landed on. One drag is one undo. Arrow keys move the cell cursor and stop at the edge. The first arrow, when nothing is selected, selects the top-left cell and does not mark it. The backslash key sets a backslash. The slash key sets a slash. Space or Enter cycles forward.Backspace or Delete clears the cell. There is no tool bar and no separate mark for an empty cell.
Press Hint for one step the numbers already force, with a sentence saying why. Hint lights the new diagonal, and it lights the numbered point that forced it, then places that one diagonal. One press writes one cell, and undo takes that press back in one step. Press Check when you want the board checked. A legal unfinished board gets "No mistakes so far. Keep going!" A broken board gets "Something breaks the rules. Look for the marked numbers or diagonals." Hint on a broken board gets "This board has a mistake, so there is no hint yet." If Hint finds nothing on a legal board, it says "No forced diagonal from here. A mark may be wrong, so try Check or Undo." Undo and Redo step through the diagonals. Reset clears every diagonal. When the diagonals match, they turn teal. The frame stays as it was. The numbered circles stay white. The dialog title is "Solved!" The dialog body is "Every cell has a diagonal, the numbers match, and nothing closes a loop." The line under the board is "Tap a cell to cycle \ / /; right-click or long-press to go back." Once the grid is solved, that line is "Every cell has a diagonal, and no loop is closed." The Mistakes counter counts how many times Check found a broken board. It is not a score.
A coral number or a coral diagonal is a clash that is already on the board. With error highlighting off, none of that coral is drawn. A number turns coral when the diagonals already drawn are too many, or when they can no longer reach the count. Those diagonals stay violet. A diagonal turns coral when it already sits on a closed loop. Print pages cannot show the yellow, the coral, or the teal.
Corners and edges
A corner numbered 1 has one cell, and that diagonal has to touch the corner. An edge numbered 2 takes both diagonals toward that point. An edge numbered 1 is fixed once the other cell is set, either toward the point or away from it. The button writes one cell and stops. A corner numbered 0 would send its diagonal away, and an edge numbered 0 would send both away. Those sentences never write on these grids. The rules still allow a 0. On a blank grid in this set the first press is the corner or the edge of 2. On the grid in the corner picture, the edge of 1 is written before the edge of 2. This article keeps the edge of 2 first.
A corner numbered 1 Easy
A corner numbered 1 has one cell. That diagonal has to touch the corner. On this blank grid the bottom-left corner is 1. The slash in row 5 column 1 touches it. A backslash there would point at the other two corners of the cell and miss this one.
A corner numbered 0 would send that same diagonal away. The button can say "This corner is 0, so the only diagonal points away from it." On these grids that sentence never writes. The rules still allow a corner 0. An edge numbered 0 would send both diagonals away. The button can say "This edge number is 0, so both diagonals point away from it." On these grids that sentence never writes either.
The new slash is yellow. The 1 has a yellow ring. No other diagonal is on the board. The grid is still unfinished. This is the opening press. The toast is "This corner is 1, so the only diagonal has to touch it." Every label returns this hint. It does not finish. The next press on this grid is the edge of 1, further down. The edge of 2 comes after that. Some grids in this set open on the edge of 2 instead, and the button marks a corner later. Some grids finish on this sentence. The live button skips that toast.
The bottom-left corner is 1, so row 5 column 1 is a slash. The new diagonal is yellow. The 1 has a yellow ring. Nothing else is filled.
An edge numbered 2 Easy
An edge numbered 2 has two cells, and both diagonals have to touch that point. On this grid the point is on the bottom edge, between row 5 column 4 and row 5 column 5. Both cells are empty. The backslash in row 5 column 4 touches the point. The slash in row 5 column 5 would touch it too.
The sentence says both diagonals. One press writes one cell, the earlier one. The picture shows row 5 column 4 only. Row 5 column 5 is still empty. That cell is a later press. On this grid the button then calls it a point that still needs its remaining diagonal, not this sentence, because one of the two cells is already filled. The three diagonals already on the bottom row stay violet. They have no ring. The new backslash is yellow. The 2 has a yellow ring. The grid is still unfinished. The article meets this edge before the edge of 1, which this same grid wrote earlier.
The toast is "This edge number is 2, so both diagonals point toward it." Every label returns this hint. It does not finish. An edge numbered 0 never writes on these grids. That sentence is named above. It has no figure.
The 2 on the bottom edge takes row 5 column 4 as a backslash. That diagonal is yellow, and the 2 has a yellow ring. Row 5 column 5 stays empty. The three slashes already on the row stay violet.
An edge numbered 1 Easy
An edge numbered 1 has two cells. Once one of them is set, the other one is fixed. On this grid the 1 is on the bottom edge, between row 5 column 1 and row 5 column 2. The corner cell is already a slash, and that slash touches the corner, not this 1. The remaining cell has to touch the 1, so row 5 column 2 is a slash.
The same sentence covers the other reading. When the 1 is already met, the remaining cell points away. The button says "This edge is 1, and the other diagonal is already set, so this cell is fixed." It does not use a second sentence. This figure is the reading where the cell has to touch. The corner slash stays violet. The new slash is yellow. The 1 has a yellow ring. The grid is still unfinished. This press follows the corner on this grid. The article teaches it after the edge of 2. The next press of the same sentence, on the next 1 along the bottom edge, is the same reading.
Every label returns this hint. It does not finish. Some grids finish on this sentence. The live button skips that toast. A blank grid in this set does not open here.
The corner slash does not touch this 1, so row 5 column 2 is a slash. The new diagonal is yellow. The 1 has a yellow ring. The corner slash has no ring.
The numbers
A point that already has as many diagonals as its number sends the remaining cells away. A point that still needs every empty cell takes each of those diagonals. When more than one loop-free way can meet the number, and those ways agree, the button writes the diagonal they share. A number 0 would send every remaining diagonal away. The button can say "This number is 0, so every remaining diagonal points away from it." A number 4 would take every one. The button can say "This number is 4, so every remaining diagonal has to touch it." Those sentences never write on these grids. The rules still allow a 0 and a 4. A blank grid in this set does not open on these three sentences. The mixed number is an early sentence, so an easy grid returns it when it is the next step.
The number is already met Easy
When a point already has as many diagonals as its number, every cell that is still empty around it points away. On this grid the point is 2. Two diagonals already touch it: the slash in row 5 column 3 and the backslash in row 5 column 4. Two cells are still empty, row 4 column 3 and row 4 column 4. Neither of them can touch the point. The press draws the earlier one, row 4 column 3, as a slash. That slash points away.
The sentence says the remaining cells. One press writes one cell. Row 4 column 4 is still empty. The next press of the same sentence draws that cell as a backslash, which also points away. The diagonals already on the board stay violet. The new slash is yellow. The 2 has a yellow ring. The grid is still unfinished. A blank grid in this set does not open here.
The toast is "This point already has its diagonals, so the remaining cells point away." Every label returns this hint. It does not finish. Some grids finish on this sentence. The live button skips that toast. A number 0, which would send every remaining diagonal away from the start, never writes on these grids. That sentence is named in the lead. It has no figure.
The 2 already has two diagonals, so row 4 column 3 points away. The new slash is yellow. The 2 has a yellow ring. Row 4 column 4 stays empty.
Every remaining cell Easy
When the empty cells around a point are exactly the diagonals it still needs, each of those diagonals has to touch it. On this grid the point is 3. The slash in row 3 column 2 is already drawn, and it does not touch this point. Three cells are still empty: row 2 column 1, row 2 column 2, and row 3 column 1. All three have to touch the 3. The press draws the earliest one, row 2 column 1, as a backslash.
The sentence says each remaining diagonal. One press writes one cell. The other two stay empty. The next press is the same sentence on the same point, and it draws row 2 column 2. The diagonals already on the board stay violet. The new backslash is yellow. The 3 has a yellow ring. The grid is still unfinished. A blank grid in this set does not open here.
The toast is "This point still needs every remaining diagonal, so each one has to touch it." Every label returns this hint. It does not finish. Some grids finish on this sentence. The live button skips that toast. A number 4, which would take every diagonal around an interior point, never writes on these grids. That sentence is named in the lead. It has no figure.
The 3 still needs every empty cell, so row 2 column 1 is a backslash. That diagonal is yellow. The 3 has a yellow ring. The other two cells stay empty.
Every way agrees Easy
A point can still be met in more than one pattern, and the patterns that are left can agree on a diagonal. On this grid the point is 3. Two diagonals already touch it: the backslash in row 2 column 2 and the slash in row 3 column 2. Two cells are still empty, row 2 column 3 and row 3 column 3. The 3 needs one more touch, so one of those cells has to point toward it and the other has to point away. The pairing that puts a slash in both cells would meet the count, and it would also join two points that are already connected, so it is not a remaining way. The only remaining way puts a backslash in both cells. The button writes the earlier cell, row 2 column 3.
The sentence says the diagonals the ways agree on. One press writes one cell. Row 3 column 3 stays empty in this picture. The next press on this grid is a different sentence, a met number. The diagonals already on the board stay violet. The new backslash is yellow. The 3 has a yellow ring. The grid is still unfinished. This picture is from a medium grid that opened on a corner. A blank grid in this set does not open here. This sentence is one of the early sentences. An easy grid returns it. The 5×5 easy walks do not reach it. Some larger easy walks do.
The toast is "Every way to meet this number agrees on these diagonals." Every label returns this hint. It does not finish. The same sentence comes up again on this grid, on a different point.
The only loop-free way to finish the 3 puts a backslash in row 2 column 3. That diagonal is yellow. The 3 has a yellow ring. Row 3 column 3 stays empty.
A loop
One diagonal would join two points that are already connected, so the cell takes the other diagonal. The button writes that one cell. It is never an opening. On many grids it is the last press, and the live button skips that toast. The figure leaves one cell empty. The two points on that figure have no numbers, so the yellow is the new diagonal and there is no ring.
The other diagonal Easy
If one diagonal would join two points that are already connected, the cell takes the other diagonal. On this 10×8 grid, row 2 column 5 is empty. A backslash there would join two points that are already joined, through the slash in row 1 column 5, the backslash in row 1 column 6, and the slash in row 2 column 6. The cell takes the slash.
Neither of those two points has a number. The live board draws a yellow ring only on a numbered point, so this picture has no ring. The new slash is yellow. The three diagonals that already join the two points stay violet. Every loop hint in this set has the same gap: both ends of the rejected diagonal are unnumbered. The grid is still unfinished. One cell, row 7 column 5, is still empty. This is not the last press. The last press on this grid is also this sentence, and it solves, so the live button skips that toast. The 5×5 grid in the earlier pictures ends on this sentence too, and that press solves. A blank grid in this set does not open here.
The toast is "Drawing a \ here would join two points that are already connected, so this cell is /." Every label returns this hint. It does not finish. This board is the tall 10×8. The 5×5 pictures stay at the ordinary size.
A backslash in row 2 column 5 would close a loop, so the cell is a slash. The new diagonal is yellow. There is no ring. The path through row 1 column 5, row 1 column 6, and row 2 column 6 stays violet. Row 7 column 5 stays empty.
Two clues
Two clues that share a side can still be drawn in more than one way, and those ways can use the same diagonal in one cell. The button writes that cell. The same idea for two 1s that sit on a diagonal never writes on these grids. The sentence about two open cells that cannot point the same way never writes. The sentence about one diagonal that breaks a number or closes a loop never writes. The sentence about both choices forcing the same diagonal never writes. The button does not issue those three. A blank easy grid never says the adjacent-clues sentence. A medium grid can open on it, or on a corner, or on an edge of 2. An easy grid returns nothing for this sentence.
Two adjacent clues Medium
Two numbers that share a side can still be drawn in more than one way. When every one of those ways uses the same diagonal in one cell, that cell is fixed. On this blank grid the two 1s are the point on the left edge and the point just inside it. Four cells touch them: row 1 column 1, row 1 column 2, row 2 column 1, and row 2 column 2. Two drawings meet both 1s. Both drawings put a backslash in row 1 column 2. The other three cells are not the same in both drawings, so the button does not write them.
One drawing meets the edge 1 with the slash in row 1 column 1, and meets the inner 1 with the slash in row 2 column 1. The other meets the inner 1 with the backslash in row 1 column 1, and meets the edge 1 with the backslash in row 2 column 1. In both, row 1 column 2 is a backslash, pointing away from the inner 1, and row 2 column 2 happens to be a slash. The button writes the first cell the scan agrees on, which is row 1 column 2. The new backslash is yellow. Both 1s have a yellow ring. The rest of the grid is empty. The grid is still unfinished. This is the opening press of this medium grid. The article teaches it last. A blank easy grid never says this sentence. Some medium grids open on a corner or on an edge of 2 instead, and the button reaches this sentence later.
The same scan can look at two 1s that sit on a diagonal. The button can say "Every remaining drawing of these two diagonal 1s uses the same diagonal here." On these grids that sentence never writes. Two further ideas sit past the ceiling the button uses. Two open cells can be unable to point the same way. The button can say "These two open cells cannot point the same way, and the rest of the board fixes this one." One diagonal in a cell can break a number or close a loop. The button can say "One diagonal in this cell breaks a number or closes a loop, so the other diagonal stays." Both choices for a cell can force the same diagonal somewhere else. The button can say "Both choices for that cell force the same diagonal here." The button does not say those sentences on these grids. They have no figures.
The toast is "Every remaining drawing of these two adjacent clues uses the same diagonal here." An easy grid returns nothing. Medium returns this hint, and so does any label past easy. It does not finish. The stored grid is medium.
Both ways to meet the two adjacent 1s put a backslash in row 1 column 2. That diagonal is yellow. Both 1s have a yellow ring. The rest of the grid is empty.
Common mistakes
Check paints a broken rule. Hint will not explain a board that is already broken. The toast is "This board has a mistake, so there is no hint yet." Check says "Something breaks the rules. Look for the marked numbers or diagonals." A wrong diagonal can also sit there with no coral at all. Then Check says "No mistakes so far. Keep going!" If the marks still force a step, Hint offers it. The wrong diagonal stays, and the new diagonal is the one that turns yellow. If the wrong diagonal leaves no forced step, Hint says "No forced diagonal from here. A mark may be wrong, so try Check or Undo." The button does not call the hint on a broken board. The figures of a broken board do not draw yellow. With error highlighting off, the same clashes paint nothing coral.
Row 1 column 1 is a slash and row 1 column 2 is a backslash. Both touch the 1 between them. That number is coral: a soft fill, a coral stroke, and a coral numeral. Both diagonals stay violet. No other point. No cell. No yellow. Hint says "This board has a mistake, so there is no hint yet."
Row 5 column 1 is a backslash. The bottom-left corner is 1, and this is the only cell. The backslash points away, so the 1 cannot be met. The number is coral. The diagonal stays violet. No cell turns coral. No yellow.
Row 3 column 1 is a slash, row 3 column 2 is a backslash, row 4 column 1 is a backslash, and row 4 column 2 is a slash. Those four diagonals are one cycle, and they are coral. The centre point of the four cells has no number. No number turns coral. No yellow.
Row 1 column 3 is a slash. The solution diagonal there is a backslash. Before the hint the board is legal and unfinished. Check says "No mistakes so far. Keep going!" The slash is not coral. Hint still marks the bottom-left corner. The picture is after that hint. The wrong slash stays violet, with no ring. The new slash on row 5 column 1 is yellow, with a yellow ring on the corner. No coral.
Row 5 column 2 is a backslash. The solution diagonal there is a slash. Nothing else is added. The board is legal and unfinished. Check says "No mistakes so far. Keep going!" The backslash is not coral. Hint has nothing to place, on an easy grid or any other label. The button says "No forced diagonal from here. A mark may be wrong, so try Check or Undo." That is not the error toast. No yellow. The wrong backslash stays violet.
What to play next
Easy grids follow from a corner of 1, an edge of 2, an edge of 1, a point that already has its diagonals, and a point that still needs every remaining cell. Some easy sizes also use the mixed number, and some use the other diagonal. The button uses a separate sentence for each of those. It never says that a corner is 0, that an edge is 0, that a number is 0, or that a number is 4. Those numbers are not on these grids. The rules still allow them. Start on a 5×5 easy grid, or on the daily 7×7 easy grid. Medium grids add the diagonal that two adjacent clues share. A medium grid can still open on a corner or on an edge of 2, and it can come back to an early sentence. The sentence about two diagonal 1s does not come up as its own hint. The three sentences past that one do not come up either. An easy grid does not return the adjacent-clues sentence. An easy grid in this set finishes before that sentence. An easy grid does return the mixed number, and the other diagonal, when those are the next step.
A printed puzzle page shows the grid and the numbered circles. A printed answer draws each diagonal as a thick line under the circles. Four 5×5, 6×6, or 7×7 grids share a sheet. Two 8×8, 9×9, 10×10, 8×6, or 10×8 grids share a sheet. Large print is one grid on the sheet. The printable page isSlant packs.
- Easy5×5A corner of 1, an edge of 2, an edge of 1, a met number, and a number that still needs every cell. One of these grids also ends on the other diagonal. That press solves, so the live button skips the toast. They do not say the mixed number, or the two adjacent clues. They open on a corner or on an edge of 2. The corner, both edges, the met number, the number that still needs every cell, and the mistake pictures are one of these grids.Play 5×5 →
- Easy6×6Those sentences. One grid also says the mixed number. One ends on the other diagonal. They do not say the two adjacent clues. They open on a corner or on an edge of 2.Play 6×6 →
- Easy7×7An edge of 2, an edge of 1, a met number, a number that still needs every cell, and the mixed number. One ends on the other diagonal. They do not say a corner of 1, and they do not say the two adjacent clues. All three open on an edge of 2. This is the daily size.Play 7×7 →Today's daily →
- Easy8×8A corner of 1 on one grid, an edge of 2, an edge of 1, a met number, a number that still needs every cell, and the other diagonal. All three end on the other diagonal. They do not say the mixed number, and they do not say the two adjacent clues. They open on an edge of 2 or on a corner.Play 8×8 →
- Easy9×9An edge of 1, a met number, and a number that still needs every cell. Two grids say an edge of 2. Two say a corner of 1. Two say the mixed number. They do not say the other diagonal, and they do not say the two adjacent clues. They open on an edge of 2 or on a corner.Play 9×9 →
- Easy10×10An edge of 2, an edge of 1, a met number, a number that still needs every cell, the mixed number, and the other diagonal. One grid also says a corner of 1. All three end on the other diagonal. They do not say the two adjacent clues. They open on an edge of 2 or on a corner.Play 10×10 →
- Easy8×6An edge of 2, an edge of 1, a met number, and a number that still needs every cell, on the tall grid. One grid says a corner of 1. Two say the mixed number. One ends on the other diagonal. They do not say the two adjacent clues. They open on a corner or on an edge of 2.Play 8×6 →
- Easy10×8An edge of 2, an edge of 1, a met number, a number that still needs every cell, and the other diagonal, on the tall grid. One grid also says a corner of 1 and the mixed number. All three end on the other diagonal. They do not say the two adjacent clues. All three open on an edge of 2. The other-diagonal picture is one of these grids.Play 10×8 →
- Medium5×5An edge of 1, a met number, a number that still needs every cell, and the two adjacent clues. One grid also says a corner of 1 and the mixed number. They do not say an edge of 2, and they do not say the other diagonal. They open on the two adjacent clues or on a corner. The two-clues picture is one of these grids. The mixed-number picture is another.Play 5×5 →
- Medium6×6An edge of 1, a met number, a number that still needs every cell, and the two adjacent clues. Two grids say a corner of 1. They do not say an edge of 2, the mixed number, or the other diagonal. They open on a corner or on the two adjacent clues.Play 6×6 →
- Medium7×7An edge of 1, a met number, a number that still needs every cell, and the two adjacent clues. One grid says an edge of 2. One says a corner of 1. They do not say the mixed number, and they do not say the other diagonal. They open on an edge of 2, a corner, or the two adjacent clues.Play 7×7 →
- Medium8×8An edge of 1, a met number, a number that still needs every cell, and the two adjacent clues. One grid also says an edge of 2 and the mixed number. One says a corner of 1. They do not say the other diagonal. They open on the two adjacent clues, a corner, or an edge of 2.Play 8×8 →
- Medium9×9A corner of 1 on one grid, an edge of 1, a met number, a number that still needs every cell, and the two adjacent clues. One grid also says the mixed number. They do not say an edge of 2, and they do not say the other diagonal. They open on the two adjacent clues or on a corner.Play 9×9 →
- Medium10×10An edge of 1, a met number, a number that still needs every cell, and the two adjacent clues. They do not say a corner of 1, an edge of 2, the mixed number, or the other diagonal. All three open on the two adjacent clues.Play 10×10 →
- Medium8×6An edge of 1, a met number, a number that still needs every cell, and the two adjacent clues, on the tall grid. One grid says an edge of 2. Two say a corner of 1. One says the mixed number. They do not say the other diagonal. They open on an edge of 2 or on a corner.Play 8×6 →
- Medium10×8Those sentences, including the two adjacent clues, on the tall grid. Two grids say an edge of 2. Two say the mixed number. One says a corner of 1. They do not say the other diagonal. They open on a corner, the two adjacent clues, or an edge of 2.Play 10×8 →
There is no guide-sized seed to open. The boards above are teaching boards.