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2020 Cono Sur Olympiad
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Part of
2020 Cono Sur Olympiad
Problems
(1)
2020 Cono Sur Math Olympiad P6
Source: Cono Sur Math Olympiad 2020
12/4/2020
A
4
4
4
x
4
4
4
square board is called
b
r
a
s
u
c
a
brasuca
b
r
a
s
u
c
a
if it follows all the conditions: • each box contains one of the numbers
0
,
1
,
2
,
3
,
4
0, 1, 2, 3, 4
0
,
1
,
2
,
3
,
4
or
5
5
5
; • the sum of the numbers in each line is
5
5
5
; • the sum of the numbers in each column is
5
5
5
; • the sum of the numbers on each diagonal of four squares is
5
5
5
; • the number written in the upper left box of the board is less than or equal to the other numbers the board; • when dividing the board into four
2
2
2
×
2
2
2
squares, in each of them the sum of the four numbers is
5
5
5
.How many
"
b
r
a
s
u
c
a
s
"
"brasucas"
"
b
r
a
s
u
c
a
s
"
boards are there?
combinatorics