## 5.2: Isn't it Romantic? (Solution)

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```Author: Roger Barkan

Solution written by Chris(?):

One first identifies that the words are the adjectival forms of names of
metals (gold, silver, tin, copper, nickel) in five Romance languages
(Latin, Italian, Spanish, Portuguese, French).

Consider the names of these five metals in each of the five languages,
or 25 words in all. It turns out there is a unique way to put one of
these words in each square, starting with the words given, so that no
two words of the same language or meaning lie in the same row or column.
(Mathematicians call such an arrangement a "Latin square".) The word that
goes in the bottom right corner is the Spanish word for the adjective
"gold", which is DORADO. (We know, DORADO is more properly translated
as "gilded". So sue us.)

From Roger:

Shown are words, in adjective form, for five different metallic elements
(gold, silver, copper, nickel, and tin) in five different Romance Languages
(Italian, Spanish, French, Portuguese, and Latin).  The fact that these are
specifically Romance Languages, plus the title, hint that the entire puzzle
is a "Latin square".  "Latin square" is a mathematical term for a square
where every element is used exactly once in each row and column.  There is
a unique way to fill in the 25 element/language pairs into the grid with
the ones already given so that every row and column contains every element
and language exactly once.  When this is done, the word in the golden
square is the Spanish word for golden, DORADO.

LG SC IS PT FN

PN FG LC SS IT

FS LT SN IG PC

ST IN PG FC LS

IC PS FT LN SG

```