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2012 CHMMC Fall
10
2012 Fall Team #10
2012 Fall Team #10
Source:
March 20, 2022
number theory
Problem Statement
Let
N
=
(
2
2012
0
)
(
2
2012
1
)
(
2
2012
2
)
(
2
2012
3
)
.
.
.
(
2
2012
2
2012
)
.
N = {2^{2012} \choose 0} {2^{2012} \choose 1} {2^{2012} \choose 2} {2^{2012} \choose 3}... {2^{2012} \choose 2^{2012}}.
N
=
(
0
2
2012
)
(
1
2
2012
)
(
2
2
2012
)
(
3
2
2012
)
...
(
2
2012
2
2012
)
.
Let M be the number of
0
0
0
’s when
N
N
N
is written in binary. How many
0
0
0
’s does
M
M
M
have when written in binary? (Warning: this question is very hard.)
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