
Flash player supportDue to deprecation of Flash at the end of 2020 we are converting all our games to HTML5 which is supported by all popular browsers. We are planning to complete this process before the end of 2019. In the meantime, in case you have problems enabling Flash on your browser please see these instructions Skyscrapers techniquesSkyscrapers is a building placing puzzle based on an NxN grid with some clues along its sides. The object is to place a skyscraper in each square, with a height between 1 and N, so that no two skyscrapers in a row or column have the same number of floors. In addition, the number of visible skyscrapers, as viewed from the direction of each clue, is equal to the value of the clue. Note that higher skyscrapers block the view of lower skyscrapers located behind them. In the example below we have a 5x5 Skyscrapers puzzle with five columns and five rows. We now need to place 1floor to 5floor skyscrapers in each row and column according to the above rules… but how? Starting techniquesSkyscrapers puzzles frequently contain the clue 1 and/or clue N which are very easy to start off with. Clue 1 means only the highest skyscraper in the row or column is visible and clue N means all skyscrapers in the row or column are visible: 1. Clues of 1Clue 1 means only one skyscraper is visible when viewing the row or column from the direction of the clue. Therefore in the example below, the highest skyscraper with 5 floors must be placed next to the clue 1 to block the view of the remaining buildings. 2. Clues of NClue N, in an NxN grid, means all skyscrapers are visible when viewing the row or column from the direction of the clue. Therefore in the example below, the five skyscrapers must be placed in ascending order from the clue 5 so no building gets blocked. Basic techniquesWe now continue with the basic techniques, where it is usually straightforward to analyze and deduct where the next skyscraper should be placed. Here are some ways of using the basic techniques: 1. High skyscrapers (technique 1)The next step after starting techniques is usually placing one or more of the highest skyscrapers. Let’s look at the center column of the partially solved puzzle below. According to the rules, 4 skyscrapers should be visible when looking from the direction of clue 4 on the bottom which means a 5floor skyscraper can only be placed in one of the two top squares. However, since the top row already contains a 5floor skyscraper, the only square in the center column in which such skyscraper can be placed is the second from the top. 2. High skyscrapers (technique 2)Sometimes the information of two or more clues is necessary to determine where to place the next skyscraper. Let’s look where a 4floor skyscraper can be placed in the top row of the partially solved puzzle below. This is not possible in the left square since the clue 3 on the left requires that three skyscrapers are visible from the left of the top row. Similarly, this is not possible in the right square since the clue 4 on the top requires that four skyscrapers are visible from the top of the right column. Since the second column from the left already contains a 4floor skyscraper, the only square in the top row where such skyscraper can be placed is in the center. 3. Unique skyscraper sequencesThere are sometimes situations where only one sequence of remaining skyscrapers can be placed in the empty squares of a row or column. The far right column of the partially solved puzzle below is missing skyscrapers with 2, 3, 4 and 5 floors. Whichever way we try to place these four skyscrapers, we will find that clue 4 leaves us with only one possible sequence as shown in the righthand image below. 4. No skyscraper may repeat in a row or columnIn many cases, especially after several steps in a puzzle have been completed, it is possible to progress using the second rule of Skyscrapers where no two skyscrapers in a row or column can have the same number of floors. Using this rule, we can see that a 4floor and a 5floor skyscraper can be placed in the second and fourth rows respectively as shown below. After this, a 4floor skyscraper can be placed in the third row using the same rule. 5. Highest skyscraper located faropposite clue 2Whenever the highest skyscraper is at the far opposite side of clue 2, the second highest skyscraper must be placed next to clue 2. In the example below, a 4floor skyscraper which is the second highest in a 5x5 grid must be placed next to clue 2 in the top square of the left column. Any other skyscraper would cause more than two buildings to be visible when viewing the left column from the direction of this clue. 6. Lowest skyscraper located adjacent to clue 2Whenever a 1floor skyscraper is adjacent to clue 2, the next square must contain the highest skyscraper. In the example below, a 5floor skyscraper which is the highest in a 5x5 grid must be placed in the second square of the bottom row. Any other skyscraper would cause more than two buildings to be visible when viewing the bottom row from the direction of the clue. 7. Second highest skyscraper in secondsquare from clue 2It is impossible to place the second highest skyscraper in the second square from clue 2. For example, let’s try placing a 4floor skyscraper in the second column as shown in the left image below. We can immediately see this is impossible because any skyscraper we place above it will cause either one skyscraper or three skyscrapers to be visible when viewing the column from the direction of the clue. Advanced techniquesThe techniques described so far won’t be enough to solve more difficult puzzles. At some point when solving medium and hard puzzles you will find it necessary to combine different techniques or think what might happen one or two steps ahead. For this you will need to use advanced techniques to work out many special and interesting logic situations. Here are some examples of advanced techniques. You will develop many more of your own when solving medium and hard Skyscrapers puzzles by yourself: 1. Advanced technique 1Let’s try to figure out which skyscraper should be placed in the square with the question mark below. There are two obvious possibilities, 3floor or 4floor, since any other skyscraper will violate the requirement of clue 2 on the right. However, placing a 3floor skyscraper will force us to place the 4floor skyscraper in the leftmost square of the second row which is not allowed because the left column already contains such skyscraper. Therefore, the only candidate for the square with the question mark is a 4floor skyscraper. 2. Advanced technique 2Below is another partially solved puzzle. Let’s analyze where a 4floor skyscraper can be placed in the center column. The top square is obviously not a candidate since there is already a 4floor skyscraper in the top row. However, the squares immediately above and below the 5floor skyscraper are also not candidates: placing a 4floor skyscraper in either of these squares will cause violation of clues 2 above or below this column. This means the only square in which a 4floor skyscraper can be placed is at the bottom of the center column. 3. Advanced technique 3Let’s see where a 5floor skyscraper can be placed in the righthand column. The top square is not a candidate because of clue 2 and the bottom square is not a candidate either because there is already a 5floor skyscraper in that row. But what about the second and third squares from the top? If we place a 5floor skyscraper in the second square of the righthand column then we would have to place a 4floor skyscraper in the left square of the second row to comply with clue 2 on the left. However, the lefthand column already contains a 4floor skyscraper so this option is not possible either. This means the third square in the righthand column is the only candidate in which a 5floor skyscraper can be placed. 4. Advanced technique 4We now look which skyscraper can be placed in the second square of the righthand column in the puzzle below. Since 4floor and 5floor skyscrapers are already placed in the respective row and column the remaining candidates are 1floor, 2floor and 3floor skyscrapers. If we try to place a 1floor skyscraper we immediately see it is not possible to comply with clue 3 on the right. Whichever way we try to arrange the skyscrapers we can’t make 3 buildings visible when viewed from that direction. On the other hand, if we try to place a 3floor skyscraper we are forced to place a 4floor skyscraper above it which is not possible due to the requirements of clue 3 in the topright corner. Therefore the only candidate for this square is a 2floor skyscraper 5. Advanced technique 5Looking at the bottom row of the partially solved puzzle below we see the two squares on the right can only be 1floor and 2floor skyscrapers though we don’t know in which order. Any other skyscraper cannot be placed because of the two clues of 4. This leaves 3floor, 4floor and 5floor skyscrapers as the remaining candidates for the center square of the bottom row. A 3floor skyscraper is obviously not possible because the center column already contains a building with this height. A 5floor skyscraper is also not possible either, because this will conflict with clue 4 on the right. This means the only remaining candidate for the center square in the bottom row is a 4floor skyscraper. 6. Advanced technique 6In the righthand column of the puzzle below, the third square can only be a 1floor or 2floor skyscraper. Any higher skyscraper will conflict with clue 4 on the right. This means the 4floor and 5floor skyscrapers can only be placed in the two top squares of this column though we don’t yet know in which order. However, if we try placing the 4floor skyscraper in the top square, we will quickly find there is no way to place the remaining skyscrapers without violating the requirements of clue 4 on the bottom. This means the top square of the righthand column must contain a 5floor skyscraper followed with a 4floor skyscraper under it. 