MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
Bosnia and Herzegovina IMO TST
2022 Bosnia and Herzegovina IMO TST
4
4
Part of
2022 Bosnia and Herzegovina IMO TST
Problems
(1)
Bosnia and Herzegovina 2022 IMO TST P4
Source:
5/22/2022
In each square of a
4
×
4
4 \times 4
4
×
4
table a number
0
0
0
or
1
1
1
is written, such that the product of every two neighboring squares is
0
0
0
(neighboring by side).
a
)
a)
a
)
In how many ways is this possible to do if the middle
2
×
2
2\times 2
2
×
2
is filled with
4
4
4
zeros?
b
)
b)
b
)
In general, in how many ways is this possible to do (regardless of the middle
2
×
2
2 \times 2
2
×
2
)?
combinatorics
counting