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National and Regional Contests
Russia Contests
Soros Olympiad in Mathematics
VII Soros Olympiad 2000 - 01
8.10
8.10
Part of
VII Soros Olympiad 2000 - 01
Problems
(1)
numbers 0,1,-1 in 2nx2n board (VII Soros Olympiad 2000-01 R1 8.10)
Source:
7/27/2021
Place in the cells the boards measuring: a)
2
×
2
2 \times 2
2
×
2
, b)
4
×
4
4 \times 4
4
×
4
, c)
2
n
×
2
n
2n \times 2n
2
n
×
2
n
, numbers
0
0
0
,
1
1
1
and
−
1
-1
−
1
so that in each case all the sums of numbers in rows and columns are different.
combinatorics