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35
2016 Guts #35
2016 Guts #35
Source:
December 24, 2016
Problem Statement
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
M
a
x
i
m
a
l
D
e
t
e
r
m
i
n
a
n
t
)
<
/
s
p
a
n
>
<span class='latex-bold'>(Maximal Determinant)</span>
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
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a
x
ima
l
De
t
er
minan
t
)
<
/
s
p
an
>
In a
17
×
17
17 \times 17
17
×
17
matrix
M
M
M
, all entries are
±
1
\pm 1
±
1
. The maximum possible value of
∣
det
M
∣
\left| \det M \right|
∣
det
M
∣
is
N
N
N
. Estimate
N
N
N
.An estimate of
E
>
0
E > 0
E
>
0
earns
⌊
20
min
(
N
/
E
,
E
/
N
)
2
⌋
\left\lfloor 20\min(N/E, E/N)^2 \right\rfloor
⌊
20
min
(
N
/
E
,
E
/
N
)
2
⌋
points.
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