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Embassy Park - A Grid Deduction Puzzle

Puzzling Asked on July 4, 2021

An entry in Fortnightly Topic Challenge #45: Flags


This grid deduction puzzle is a variation on the OP’s previous Office Park puzzle. You are given a set of seven buildings, which are tetracubes, 3-dimensional shapes comprised of 4 cubes each, to place in a grid. Buildings must be placed without cantilevers, so there cannot be "air" underneath a hanging cube. Buildings must be placed so that no two buildings are touching, not even diagonally, and such that the empty squares form one orthogonally connected region.

But these are not just buildings…they are embassies of Albania, Morocco, Nigeria, Somalia, Tunisia, Ukraine, and Vietnam, and being embassies, each flies one instance of its national flag on a flagpole atop one segment of its building. You must also place the flags on each building.

There are two types of clues given which describe the arrangement of the embassies and flags. The numeric clues indicate the number of buildings that can been "seen" looking along the associated row/column. A building is seen if one of its cubes, or its flag, is the first item at its height or higher to occur when looking down the row/column; treat flags as being half as high as cubes, so that a flag on a 1 cube high segment obscures another flag on a 1 cube high segment behind it, but not a 2 cube high segment.

The color clues indicate a color seen on the highest flag visible from that direction along the row/column, which may or may not be the first flag seen in that direction. The color indications are:

  • R – red
  • G – green
  • Y – yellow
  • W – white
  • BL – blue
  • BK – black
  • NF – no flag is visible from this vantage point

As an example, we might have the following embassy placement and cluing:
enter image description here

[For the color blind, the 1 in column one is shaded yellow and blue to indicate Ukraine’s flag, the 2 in column five is shaded white and green to indicate Nigeria’s flag, and the 1 in column eight is shaded black and red to indicate Albania’s flag.]

From the left, only one building is visible (even though we see two different tiers of it). The only flag visible from the left is Ukraine’s, and yellow is one of the colors on it. From the right we can see three buildings: 1+ of the Albanian embassy, 2+ of the Nigerian embassy, and 3 from the Ukrainian embassy. The highest flag seen from the right is Nigeria’s (being on a 2 cube high stack), so green is a color seen in it.

Ready? Here’s the grid to be solved:

Grid

Solver Helps

HINT

Pieces

I
  1111 or 4

L
  31 or 112 or 111
                 1

O
  22 or 11
        11

T
  121 or  1
         111

V (this is the one that has left- and right-handed versions)
  12 or 11
  1     2

W
  12
   1

S
  11  or  11
   11    11

TEXT VERSION

      G |N F| W |N F|N F| Y |N F| R 
      2 |   |   |   |   |   |   |   
    ---------------------------------
G   |   |   |   |   |   |   |   |   |1 W
    ---------------------------------
NF  |   |   |   |   |   |   |   |   |3 BL
    ---------------------------------
NF  |   |   |   |   |   |   |   |   |1 NF
    ---------------------------------
R  1|   |   |   |   |   |   |   |   |  Y 
    ---------------------------------
BL  |   |   |   |   |   |   |   |   |3 R 
    ---------------------------------
NF  |   |   |   |   |   |   |   |   |  NF
    ---------------------------------
R   |   |   |   |   |   |   |   |   |3 R 
    ---------------------------------
R   |   |   |   |   |   |   |   |   |2 BK
    ---------------------------------
        |   | 2 |   | 2 | 2 |   | 1
      R |N F|B K|N F| R |B L|N F| Y

One Answer

First of all,

Step 2:

Step 3:

Step 5:

Step 6:

Correct answer by Alaiko on July 4, 2021

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