This problem combines the familiar Skyscraper puzzle with Sudoku. The board is a basic Sudoku set-up, with each digit from 1 through 9 appearing once in every row, column and each of the nine 3x3 cell blocks. Only one starting number (the '3' in the middle cell of the board), is provided.

The final grid numbers 1 through 9 also represent the unit height (e.g. storeys) of the building sitting on each cell. So in true Skyscraper fashion, the outer numbers provided around the grid indicate the number of buildings that are visible when viewed inwardly across, up or down the respective row or column, or diagonally from the four corners.

Have fun with this one! It's tougher than it might first appear! (Hint: Some digits will be duplicated along the two diagonals, so this isn't a Sudoku 'X' problem!)

4	2	5	2	1	2	3	3	4	4	3
4										4
1										3
3										2
2										4
3					3					2
4										2
9										1
3										3
2										4
3	5	1	2	8	2	2	3	3	2	3

This puzzle seems to be modified a little from Skyscraper puzzle.  However, Skyscraper puzzle has a little deficency in the sense that a person stands on a fixed position to view the building on the far distance.  The number of building that could be viewable might well differ depends on the thickness of each building, ie. the 9-storey could be blocked by the front building & could not be viewable due to the blocking of the front building due to each block of the building is too broad.  However, the 9-storey building could be viewable with more storeys if each block is too narrow.  Thus, the thickness of the building causes the computation of the number of storeys to be viewable is certainly uncertainty.

The viewing from a fixed point to the top of each building forms a triangle visualisation.  Thus, the number of building from the back of the building that could be visible varies from distance and could not be determined especally to length and breadth of the building.  For instance, the top of the 9-storey building could be exceeded 5 storeys more than the front building.  However, it turns up to be fewer than 5 storeys to be viewable from the front building as a result of the breadth & length as well as high of the building.

Nevertheless, the high, length and breadth of the building would cause the number of the storeys to be visible when standing at a fixed point.  Not only that, the distances from building to building could be caused the number of the storeys to be visible.  Based on the above analyses, the solution is uncertainty.

Posted by Lloyd Peter on 2009-02-28 23:26:48