Magic rectangles
--- Introduction ---
A
magic square
is a table of n rows and n columns, filled by numbers 1, 2, ..., n
^{2}
, such that the sums of each row and each column are equal.
Magic rectangles is a variation of this principle: you are before a table of
2
3
4
5
6
7
8
rows and
2
3
4
5
6
7
8
colomns, with a given number at the side of each row and each column. Your goal is to fill this table using the numbers par les nombres 1,2,...,lignes×colonnes, so that the
sum
product
of each row and each column equals the corresponding given number. And of course no number can be used twice.
And you should solve each problem within
0.5
1
1.5
2
3
4
5
7
10
15
20
30
minutes.
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