You are looking down at a map of a 5x5 block area of a city where each block is occupied by one skyscraper. Call the heights 1, 2, 3, 4 and 5 (say they are in 10-story increments). Each row has one of each height and each column also has one of each height.
Considering that when viewed from outside the row or column, the nearer buildings of taller height hide those behind them that are of shorter height, numbers have been placed in the yellow areas pointing to a given row or column. Each number represents the number of buildings that can be seen from that vantage point when looking at the row or column in question.
Fill in each block's height.
From Mensa Puzzle Calendar 2019 by Fraser Simpson, Workman Publishing, New York. Puzzle for December 9.
45312
12453
34521
23145
51234
Explanation
I found it convenient to copy the 5x5 grid onto an Excel worksheet, occupying cells B2:F6. Cells A3, A4, A5, C7, F7, G2, G4 contain the starting facts. (The sheet then looks exactly as in the puzzle image).
Next, I derive new facts about the contents of each cell. I number each new fact. (There are 38 according to my reckoning). These numbers are called up as reason for further steps:
STEP REASON CONCLUSION
1 A4 & G4 D4=5
2 A4 & G4 C4=4 or E4=4
3 C7 C2=5 or C3=5
4 B2 C3<>5
5 3 & 4 C2=5
6 A5 E5=5 or F5=5
7 E7 E5<>5
8 6 & 7 F5=5
9 1 & 5 & 8 B6=5 or E6=5
10 E7 E6<>5
11 9 & 10 B6=5
12 1 & 5 & 8 & 11 E3=5
13 C7 & 5 C3=4 or C4=4
14 13 & A3 C4<>4
15 13 & 14 C4=4
16 C7 & 5 & 15 C5=2 or C5=3
17 A3 & 12 C3=2 or C3=3
18 5 & 15 & 16 & 17 C6=1
19 A3 & A4 & 15 & 11 B2=4
20 A3 B3=1 or B3=2
21 A5 B5=1 or B5=2
22 11 & 19 & 20 & 21 B4=3
23 G4 & 1 & 15 & 21 F4=1
24 G4 & 1 & 15 & 21 E4=2
25 E7 & 12 & 24 & 27 E6=3
26 E7 & 12 & 24 & 27 E5=4
27 12 & 24 & 25 & 26 E2=1
28 G2 & 5 & 19 & 28 F2=2
29 G2 & 5 & 19 & 28 D2=3
30 11 & 18 & 25 & 28 F6=4
31 8 & 23 & 28 & 30 F3=3
32 11 & 18 & 25 & 30 D6=2
33 5 & 15 & 18 & 31 C3=2
34 5 & 15 & 18 & 33 C5=3
35 8 & 26 & 34 & 32 D5=1
36 8 & 26 & 34 & 35 B5=2
37 11 & 19 & 22 & 36 B3=1
38 1 & 29 & 32 & 35 D3=4
Edited on January 27, 2020, 2:30 pm
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Posted by FrankM
on 2020-01-27 14:15:29 |
Solution with explanation
