Rules
Skyscrapers is a number grid. Fill each row and each column with the heights once: 1 through N, and N is the side. A 4×4 uses 1–4. The daily puzzle is a 5×5 and uses 1–5. Play runs from 4×4 to 6×6, each in easy, medium, and hard.
A number outside the grid counts how many skyscrapers you can see from that side. A taller one hides every shorter one behind it. A clue of 1 sees only the tallest, so the tallest stands next to it. A clue of N sees every height, so they rise 1, 2, 3 and on from that side. An empty edge has no clue. No cell starts filled. The grid is finished when every cell is filled, each height appears once in every row and column, and every clue sees the right count.
Sudoku is the same one-height-per-line idea. Each row and each column holds every height once. There are no boxes here. The clues are the new part.
- One of each height. Every row and every column holds 1 through N once. N is the side. A 4×4 uses 1 to 4. A 6×6 uses 1 to 6.
- A clue counts what it sees. A number outside the grid counts the heights it can see from that side. A taller one hides every shorter one behind it.
- A 1, or a clue of N. A clue of 1 sees only the tallest, so the tallest stands next to it. A clue of N sees every height, so they rise 1, 2, 3 and on from that side.
- Finished. The grid is done when every cell is filled, each height appears once in every row and column, and every clue sees the right count.
The clue of 1 to the right of row 1 sees only the 4 beside it. The clue of 4 to the right of row 2 sees 1, then 2, then 3, then 4. Every height is teal. The clues that are present are teal. Empty edges stay empty.
- Clue
- Your height
- Notes
- Clue met
Tap a cell. Its row and column are tinted, the clues at both ends light violet, and every cell with the same height is a little darker. Type a height or use the keypad. The pad shows how many of each height are still to place. Erase, Backspace, Delete, or 0 clears the selected cell, height and notes together. Arrow keys move and stop at the edge. Notes (the Notes button, or N) are pencil marks. Shift with a digit toggles one note without turning Notes on. When you place a height, that height leaves the notes in the rest of its row and column, in the same undo step.
The line under the keypad reads "Row R, column C · N cells to go", and "1 cell to go" when one cell remains, or "Placed D · K of N on the board". With nothing selected, the pad says "Select a cell, then tap a height from 1 to N." Solved, the pad reads "Every row and column has each height once, and every clue is right." The dialog reads "Every row and column has each height once, and every clue sees the right count."
A cell turns coral when a height repeats in its row or its column, even if the line is unfinished. When a full line misses a clue, that clue turns coral and the line is tinted. The heights on that line stay violet. A clue whose full line sees the right count turns soft teal, and so does a finished row or column whose present clues match. Press Hint for one step the rules already force, with a sentence saying why. Hint lights the cell and the clues it uses. Press Check when you want the board checked. Undo and Redo step through the moves. Reset clears the grid. When the grid is complete and legal, the board turns teal: heights, clues, and frame.
- Undo
- Redo
- Notes
- Reset
- Hint
- Check
Edge clues
Start with the numbers outside the grid. A 1 and the largest clues place a height at once. The other four sections are still reading those clues.
A clue of 1 Easy
A clue of 1 sees only the tallest height, so that height stands in the nearest cell. On a 4×4 the tallest is 4. On a 5×5 it is 5. The other side of the line does not have to have a clue. This is the first press on the blank 4×4 in this section.
The clue of 1 sits to the right of row 1. From that side, the first cell is the only one the clue can see if it sees exactly one skyscraper, and that skyscraper is 4. The cell could still have been 1, 2, 3, or 4 before the write. The new 4 is violet. The rest of the row is washed a little lighter, and only this cell is ringed. Hint says "A clue of 1 sees only the tallest height, so this cell is 4."
The next press on this board is another clue of 1. The 1 to the left of row 2 puts 4 in the first cell of that row. It is not a second picture.
A clue of n Easy
A clue of N sees every height, so they stand in rising order from that side. The nearest cell is 1. The next is 2. Hint writes one of those cells at a time, starting at the near end. A clue of N on the right, or along the bottom, still puts 1 in the nearest cell. It does not put 1 at the far end. The blank 4×4 above does not open here. Its third press does. Some easy grids do open on a clue of 4, and some 5×5 medium grids open on a clue of n. This picture is that third press, not a second grid.
Two 4s are already placed, one from each clue of 1. The clue of 4 to the right of row 2 has to see 1, then 2, then 3, then 4. The nearest cell is the last cell of the row, so it is 1. That cell's list before the write is 1, 2, or 3, because 4 is already in the row. The whole row is the pattern, and the new 1 is violet. Hint says "A clue of 4 sees every height in order, so this cell is 1."
The next press writes 2 in the cell just left of that 1, still from the same clue. It is not a picture.
Clues that add up Easy
When the clues on opposite ends of a line are both present and add to N+1, the tallest height stands as many cells in from one end as that end's clue. On a 4×4, 2 and 3 add to 5. The tallest stands one cell in from the 2, which is the same cell as two cells in from the 3. This is an easy sentence. The blank grid in the picture is a medium grid, because that is where it opens. A 5×5 easy grid says the same sentence later. The 4×4 in the first sections does not say it. Not every easy grid says it.
Row 2 has 2 on the left and 3 on the right. The tallest is seen from both ends. From the left it is the second skyscraper, so it stands one cell in. From the right it is the third. Both descriptions are the same cell, and the new 4 is violet. The cell could still have been any height before the write. Both clues are lit, and the row is washed. Hint says "The clues on opposite ends add to 5, so the tallest height stands here."
A 2 opposite a 1 Easy
A clue of 2 opposite a clue of 1 puts the second tallest in the cell nearest the 2. The clue of 1 has already put the tallest at the far end, so the near cell has to be seen, and it has to be N−1. This is an easy sentence. It is not the second-tallest section later in the guide. That rule is a clue of 2 on its own. On a 4×4, 2 opposite 1 does not add to 5, so the section above does not fire. This pattern is not on the 4×4 grids. The picture is a 5×5.
Two clues of 1 have already placed the 5s: the first cell of row 1, and the last cell of row 2. Row 2 has 2 on the left and 1 on the right. The clue of 2 has to see exactly two skyscrapers. The nearest cell is seen, and with the tallest at the far end the second one is 4. The list before the write is 1, 2, 3, or 4, because 5 is already in the row. Both clues of the row are lit. Hint says "A clue of 2 opposite a clue of 1 puts height 4 in the near cell."
Too close to a clue Easy
A tall height cannot stand too close to a small clue. The first cell beside a clue of c holds at most N−c+1. Each step further in allows one more. On a 4×4, a 3 on the first cell leaves at most 2. Write the survivors as notes. The usual press crosses the tall ones off and does not fill the cell. When the cap leaves one height, Hint says "The clues around this cell leave only height D." That press is not drawn. Once a side has already seen as many heights as its clue, a taller height cannot stand further along. Hint would say "The visible count on this side is already met, so a taller height cannot stand further along." That tighter cut was not a button sentence on these grids.
The clue above column 1 is 3. Distance 0 from that clue, on a 4×4, allows at most 4−3+1, which is 2. The first cell loses 3 and 4. Pencil 1 and 2 stay. No height is written. The clue is lit, and the column is washed. No other clue touches this cell. Hint says "This cell is too close to a clue to hold 3 or 4."
A cell that is too close is an easy sentence. Not every easy grid says it. The 4×4 in the first sections does not. Some easy grids say it later. The blank grid here is a medium grid, and this is its first press.
Seen too early Easy
From a clue, count the skyscrapers that would actually be seen, not the ones a taller neighbour hides. A height that still has to be seen cannot stand so close that the count would finish early. The usual story is a tall height already placed further along. Anything shorter in front of it is seen, and it uses up a slot. The figure writes the only height the nearest cell can still be. A strike that does not fill the cell says "This height would be seen too early, so it cannot stand this close to the clue." That press is not drawn. This is an easy sentence. Not every easy grid says it. The 4×4 in the first sections does not. The notes on this figure are part of the position. They are earlier caps, stored as pencil marks.
Column 4 has a 3 below it, and a 4 already stands two cells in from the bottom. Height 3 can only sit behind that 4, so it is hidden and takes no slot. Height 2 still has to be seen. If the nearest cell were 2, the count from the bottom would be 2 and then 4, and it could not reach 3. The cell is 1. With 1 there, the cell above can be 2, and the count is 1, then 2, then 4. The pencil on that cell was 1 and 2. The 2 is struck, and the new 1 is violet. Hint says "The visible slots on this side leave only height 1 here."
One height
Once the clues have crossed heights off, a cell or a line can have only one home left.
Only one height left Easy
Cross off every height already in the row and the column. If one height is left in the cell, write it. Hint says "This cell can only be 3." It does not name the row. There is no separate sentence for the last empty cell of a line. When the cell is that last empty one, the button still says this.
The Sudoku guide already teaches this. The Sudoku sentence names the houses. This one does not.
Row 2 already holds 4, 2, and 1, from the two clues of 1 and the two writes of the clue of 4. Column 2 is still empty. The list was already only 3, so there is nothing left to cross off in the picture. The clue of 4 would have written 3 in this cell next, but the button says the single first. The ring is this cell only. The clues at both ends of the row light, and the row is not washed. The button never says the only-place sentence on this 4×4. Later presses on the same board are more of these singles. They are not separate pictures.
The only place Easy
A height that can sit in only one cell of a row, or only one cell of a column, is written there. The cell itself may still allow other heights. Those other heights have homes elsewhere in the line. Hint says "In this column, 4 fits only here." It names the row or the column, and it does not give the line a number. The ring is the cell.
The Sudoku guide teaches the same idea, and on that guide it is a medium step. Here it is one of the easy sentences. Not every easy grid uses it. The 4×4 in the first sections does not. The notes are earlier caps. The blank grid opens by crossing 3 and 4 off the second cell of column 1. This picture comes after those notes are written.
No height is filled yet. The bottom clue of 3 caps the lowest cell of column 1 at 2, and the cell above that at 3. The left clue of 3 on row 2 caps the second cell of the column at 2. None of those three cells can hold 4. The top cell is far enough from the bottom clue that the cap does not bind, so 4's only home in the column is there. That cell still shows 1, 2, 3, and 4 until the write. The new 4 is violet. The clue below the column lights. The column is not washed, because this step is a single home, not a line tint. Hint says "In this column, 4 fits only here."
That is the end of the easy sentences. An easy grid finishes with these, and not every grid uses each one. The next sections are medium. A medium grid can still finish while the button speaks only the easy sentences. One 6×6 medium grid does that: clues that add up, a clue of n, one height left, a cell too close to a clue, a height seen too early, and the only place. The button never speaks the two-heights sentence there.
Pairs
Two cells, or two heights, can claim a line. The second tallest is the other medium look, and the ladder reaches it after the pairs.
Two cells Medium
Two cells in a row or a column that can only be the same two heights claim those heights. The heights leave the other cells. The two cells stay empty. This press strikes. It does not write a height. Hint says "Two cells in this row hold the same two heights, so those heights leave the other cells." It does not name the heights or the row number.
The Sudoku guide names the digits and the line. This sentence does not. On the Sudoku guide a pair is a hard step. Here it is a medium sentence. The picture is the smallest one, on a 5×5 hard grid, after one height is filled.
The last cell of row 5 is already 5. The two cells at the right of that row can only be 1 or 2. Those heights leave the second cell of the row, which showed 1, 2, 3, and 4. The 1 and the 2 are struck. The third cell of the row also holds 1 and 2. The button stops at the first cell that holds them. The clues above and below column 2 are both 2. They belong to the cell that loses the heights, not to the pair. That column is washed. The pair cells stay on the stronger wash, because they are part of the pattern. The notes are earlier pencil marks, and they are part of this position.
Two heights Medium
Two heights that fit in only two cells of a row or a column claim those cells. The other heights leave. The strike lands inside one of the two cells. The partner can stay full until a later press. Hint says "Two heights in this column fit only two cells, so other heights leave those cells." It is a different sentence from the section above. The idea is the pair with the homes reversed. The Sudoku guide has no separate page anchor for that reversal.
One 5 is already placed, in row 1 column 2. In column 5, 4 and 5 fit only in the third and fourth cells. Every other height leaves those two cells. The first cell the pass edits is the third. It loses 1, 2, and 3, and pencil 4 and 5 stay. The fourth cell still shows 1 through 5. The clue left of row 3 is 2, and the clue above column 5 is 3. Both of those lines are washed. The notes are required. Without them, 4 and 5 are not yet trapped in two cells. Nothing is filled.
The second tallest Medium
Beside a clue of 2, the second tallest stands in the nearest cell, or somewhere strictly behind the tallest. It does not stand in the cells between the clue and the tallest, unless the nearest cell is where it belongs. On this figure the tallest is already two cells in, so the cell in front of it loses N−1 and is filled. The toast does not announce the written height. The caption does. The button tries the two pair sections before this one. The game page names the second tallest first. The same sentence covers a strike that does not fill the cell. That press is not drawn.
Row 1 already holds 4 in the third cell and 1 in the last. The clue of 2 looks from the left. Height 3 has to stand in the first cell or strictly behind that 4. The second cell is in front of the 4 and is not the first cell, so 3 leaves and 2 remains. The first cell may still be 3. Both of those cells showed 2 and 3 before the cut. The 3 on the second cell is struck, and the new height is 2. Hint says "A clue of 2 puts height 3 on the near end or strictly behind the tallest height." It does not say the cell is 2.
That is the end of the medium sentences. Hard grids add a triple, a look at the orders a line still allows, and a one-height try. A hard grid does not have to use all of them.
Hard moves
A hard grid may need three cells that share three heights, or a list of the orders one line can still be. The one-height try is the next section, on its own.
Three cells Hard
Three cells in a row or a column whose heights together are only three numbers claim those numbers. One of the three may hold just those three. The numbers leave the other cells. Hint says "Three cells in this column hold the same three heights, so those heights leave the other cells." The picture shows three cells, plus the cell that loses the heights. Nothing is filled. This needs the hard ladder, and the press is a 6×6.
The Sudoku guide teaches the same three cells. Three heights that fit only three cells would say "Three heights in this column fit only three cells, so other heights leave those cells." That sentence was not a button press on these grids.
Three 6s are already placed: row 2 column 1, row 3 column 2, and row 6 column 3. The last cells of rows 2, 3, and 6 can only be 1, 2, or 3. Those heights leave the last cell of row 1, which showed 1 through 6 before the cut. The 1, 2, and 3 are struck. The last cells of rows 4 and 5 still hold 1, 2, and 3. The button stops before them. Column 6 has no clue above or below, and row 1 has no clue on either end, so no clue chip lights and no line is washed. The notes are part of this position.
What the line still allows Hard
List the orders a line can still be, under the heights already placed and the clues at its ends. An order that sees the wrong count is dropped. If one cell is the same height in every order that remains, write it. Hint says "The orders still allowed on this line leave only height 2 here." A strike that does not fill the cell says "The orders still allowed on this line drop a height from this cell." That press is not drawn. This is a hard sentence. The whole line is the pattern.
The blank grid opens by crossing 4 off the cell under the top clue of 2 in column 3. This picture is a later step. On this grid, the first hard sentence is the orders a line still allows.
Row 2 so far is empty, empty, 4, 3. The two orders still inside those cells are 1243 and 2143. From the left, 1243 sees 1, then 2, then 4, which is three. 2143 sees 2, then 4. The 1 is hidden behind the 2, and the 3 is hidden behind the 4, so the count is two. The clue on the left is 2, so the row is 2143 and the first cell is 2. The right side has no clue. Both orders would see 2 from the right. That side does not choose. The two open cells showed 1 and 2 before the cut. The whole row is ringed, and the new 2 is violet.
What if
When the deductions above have not written a height, pick an empty cell that has two heights left and try one. If that choice breaks another line, the other height is the one that is written. Hint says "One of the two heights here contradicts the other lines, so this cell is 5." The toast does not name the height that failed. The height on the board is the one that lives. The caption names the failure. The ring is only the written cell.
If both heights live, Hint tries a different cell. If both break a line, the grid is already wrong. There is no step where both choices force the same cells. This is a hard sentence. Not every hard grid opens on a try. On the grid in the section above, the first hard sentence is the orders. On the 6×6, the first hard sentence is the three cells. The notes on this figure are part of the position.
Three heights are already placed: 5 in row 1 column 2, 4 in row 2 column 4, and 4 in row 5 column 2. The last cell of row 3 shows 4 and 5. Trying 4 makes 2 fit in only one cell of row 2, which is column 2 of that row. Writing that 2 leaves row 3 column 2 with no height. Trying 5 does not break a line. The button writes 5 and does not mention 4. Only that cell is ringed. The clue left of row 3 is 2, and the clue above column 5 is 3. They light because they touch the cell. They do not wash the row or the column.
A hard grid uses a triple, the orders a line still allows, or a one-height try when the easier sentences are not enough. It does not have to use each of them.
Common mistakes
Check marks a cell when a height repeats, even if the row is unfinished. Check marks a clue when its line is full and the seen count is wrong. A line that is not full is not a missed clue yet. A height that simply is not the finished height, and breaks nothing, stays quiet. Notes are not marked, and they do not have to be cleared.
While Check would fail, the Hint button says "This board has a mistake, so there is no hint yet." The broken pictures show the coral marks and no amber ring. The quiet wrong height shows the violet digit and the amber hint, on a different cell. Hint writes the forced height and leaves the quiet one in place. A wrong height in the cell Hint is about to fill is different: the line is not full, Check stays quiet, and applying the hint replaces that cell. All of these pictures are the same 4×4 as the first sections. Its finished first row is 3, 2, 1, 4.
Both cells of the pair turn coral. The row is not full, and the repeat is already a mistake. There is no amber ring. Hint refuses until the repeat is gone.
The top cell and the bottom cell of column 1 are both 3. The clash is the column. Both cells are coral. No amber ring. Hint refuses.
The row is filled 4, 3, 2, 1. From the right the line is 1, 2, 3, 4, and every one is a new maximum, so the seen count is 4. The clue to the right of the row is 1, so that clue turns coral and the row is tinted. The four heights stay violet. No amber ring. Hint refuses while the line is full and wrong.
A 2 in the first cell repeats nothing, and the row is not full, so no clue is missed. It stays violet. No coral. The amber ring is the opening clue of 1, on the last cell of the row, with 4 ready to write. The row is washed, and the clue of 1 on the right is lit. If Hint runs, it places that 4 and leaves the 2 where it is. A 1, or a 3, alone in that last cell is not a missed clue either. The line is not full, and applying the hint replaces it with 4.
Row 1 is filled 1, 2, 3, 4. From the right, the nearest height is 4, so the clue of 1 is met. The left of the row has no clue. Check stays quiet. It does not compare the row with the finished grid. It only checks repeats and full lines that miss a clue. All four heights stay violet. The amber ring is the next clue of 1, the first cell of row 2, with 4 ready to write. After that write, row 1 is still 1, 2, 3, 4.
What to play next
An easy grid finishes with a clue of 1, a clue of n, the tallest where two clues add to n+1, a 2 opposite a 1, a cell too close, a height seen too early, one height left, or one home in the row or the column. A medium grid adds two cells, two heights, or where the second tallest can stand, and it can also finish while the button speaks only the easy sentences. A hard grid adds a triple, the orders a line still allows, or one height tried when the other breaks. The grids in this guide are teaching boards.
- EasyClues, then one heightA clue of 1, a clue of n, the tallest where the two clues add to n+1, a 2 opposite a 1, a cell too close to a clue, a height that would be seen too early, one height left, or one home in the row or the column. Not every easy grid uses each.Play 4×4 Easy →Play 5×5 Easy →
- MediumPairs, or the second tallestThose, and sometimes two cells that claim two heights, two heights with only two cells, or where the second tallest can stand. A medium grid can also finish while the button speaks only the easy sentences.Play 4×4 Medium →
- HardA triple, a line, or a tryA triple, the orders a line still allows, or one height tried when the other breaks. Not every hard grid uses each of those.Play 4×4 Hard →
4×4 through 6×6 each come in easy, medium, and hard. The daily puzzle is a 5×5 easy grid: today's Skyscrapers and 5×5 easy. A new player can start on the 4×4 easy grid, or on the daily.
Print a Skyscrapers pack. A single pack has eight puzzles. The starter pack has nine, one of every size and setting. Four 4×4, 5×5, or 6×6 grids share a sheet. Large print is one grid. The pages are black and white. Clues print. Amber, red, teal, and notes do not.
Sudoku is one height in each row and column, and there are no boxes on this grid. Futoshiki uses signs. Renzoku uses dots.
- GuideSudokuOne height in each row and column. There are no boxes.
- GuideFutoshikiLess-than and greater-than signs between neighbours.
- GuideRenzokuDots between cells. An empty gap means not one apart.
- GuideHashiCount bridges, never cross, connect every island.
- GuideBinairoSpot pairs, fill the gaps, balance every line.
- GuideStar BattleOne or two stars in every row, column and region.
- GuideSlitherlinkDraw one loop. Start from the 0s and the 3s.
- GuideNonogramsOverlap long clues, cross the gaps, and read the crossing line.
- GuideHitoriShade repeats, never side by side, keep white connected.
- GuideNurikabeGrow each island to its number and keep one sea.
- GuideLight UpLight every cell. Start beside the 4s and 0s.
- GuideKakuroOne-way sums first, then short runs and longer lists.
- GuideKiller SudokuCage sums, then the rest of the line.
- GuideJigsaw SudokuFollow the thick walls. Each region has its own shape.
- GuideCalcudokuOne-way cages first, then the rest of the line.
- GuideShikakuEach number is an area. Start with the ones that fit one way.
- GuideMasyuTurn on black pearls, go straight through white ones.