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Skyscrapers (Posted on 2005-09-07) Difficulty: 3 of 5
Every square in the diagram below has a building of between 1 and 6 stories, inclusive.

No two buildings in any row or column have the same number of stories. Also, on one of the diagonals, no two buildings have the same number of stories, though the other diagonal has a repeat.

The numbers around the perimeter indicate the number of buildings visible when looking in the direction indicated by the arrow. Note that shorter buildings are not visible if they are behind a taller building. Determine the height of building on each square.

This puzzle was inspired by a puzzle on the Google Puzzle practice exam.

  Submitted by Bryan    
Rating: 3.9091 (11 votes)
Solution: (Hide)
Label the columns A-F from L to R, and label the rows 1-6 from top to bottom.

From the 6's shown, the third row must be 123456 while the bottom row is 654321. From the 5 given, the first column from the left must be 231456.

2xxxxx
3xxxxx
123456
4xxxxx
5xxxxx
654321

Building F1 is not a 1 or 2 and is the first of four increasing buildings from R to L, so it must be 3. E1 is either a 1 or 4, but a 1 would cause column E to have either more or less than three visible buildings, so E1 must be 4. E5 must be 6; a 6 elsewhere in column E would violate the number of visible buildings either in column E or row 4. E2 must be 1.

2xxx43
3xxx1x
123456
4xxx3x
5xxx6x
654321

B5 is neither 2 nor 5, therefor the one diagonal with numbers 1-6 must be A1-F6, making B2 4 and D4 5. D5 cannot be 6, and a 6 in D1 would not satisfy 4 visible buildings in row 1, so the 6 in column D is D2. Thus D1 is 1 and D5 is 2.

2xx143
34x61x
123456
4xx53x
5xx26x
654321

B1 cannot be 5, so C1 is 5 and B1 is 6. C2 cannot be 5, so F2 is 5 and C2 is 2. F4 cannot be 4, so F5 is 4 and F4 is 2. B4 cannot be 6, so C4 is 6 and B4 is 1. B5 is 3 and C3 is 1.

265143
342615
123456
416532
531264
654321

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2022-05-03 21:32:47
solution by computerSteven Lord2020-02-04 12:40:38
SolutionAnswerMath Man2020-01-08 17:38:23
solutionsalil2006-02-24 10:00:26
solutionsalil2006-02-23 04:10:00
I have it!Waldo Pepper2005-11-24 14:55:23
As close as I can get.....Jeramie2005-11-05 14:41:54
re: OopsPercy2005-09-07 12:01:17
OopsTan Kiat Chuan2005-09-07 10:06:13
re: Solution 2Lisa2005-09-07 09:28:08
SolutionFull SolutionLisa2005-09-07 09:26:21
SolutionSolution 2Tan Kiat Chuan2005-09-07 08:54:17
SolutionSolutionPercy2005-09-07 01:08:56
Hints/TipsTip:Percy2005-09-07 01:03:05
QuestionI think ther are 2 repeats on 1 diag?Percy2005-09-07 01:00:02
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