--         File: map_coloring.sql
--      Version: 1.1
-- Last Changed: 2020-02-27
--           by: Damir;  https://www.damirsystems.com
--      Project: Map Coloring
--  Description: Fun challenge from Decision Management Community
--               https://dmcommunity.org/challenge/challenge-may-2019/
--           DB: PostgreSQL, MS SQL Server


WITH
color AS ( -- Blue, Red, Green, Yellow
    SELECT p FROM (
        VALUES ('B'), ('R'), ('G'), ('Y')
    ) AS x(p)
),
possible AS ( -- generate 4^6 = 4096 possible combinations
    SELECT
        a.p AS BE  -- Belgium
      , b.p AS DK  -- Denmark
      , c.p AS FR  -- France
      , d.p AS DE  -- Germany
      , e.p AS LU  -- Luxembourg
      , f.p AS NL  -- Netherlands
    FROM       color AS a
    CROSS JOIN color AS b
    CROSS JOIN color AS c
    CROSS JOIN color AS d
    CROSS JOIN color AS e
    CROSS JOIN color AS f
)
SELECT BE, DK, FR, DE, LU, NL
FROM possible

WHERE (1=1) -- apply constraints

--  BE borders FR, LU, DE, NL
AND BE NOT IN (FR, LU, DE, NL)

--  DK borders DE
AND DK NOT IN (DE)

--  FR borders BE, LU, DE
AND FR NOT IN (BE, LU, DE)

--  DE borders FR, LU, BE, NL, DK
AND DE NOT IN (FR, LU, BE, NL, DK)

--  LU borders FR, DE, BE
AND LU NOT IN (FR, DE, BE)

--  NL borders BE, DE
AND NL NOT IN (BE, DE)

-- order results
ORDER BY BE, DK, FR, DE, LU, NL
;

-- Note: There are 144 solutions