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2015 ASDAN Math Tournament
36
36
Part of
2015 ASDAN Math Tournament
Problems
(1)
2015 Guts #36
Source:
8/2/2022
A blue square of side length
10
10
10
is laid on top of a coordinate grid with corners at
(
0
,
0
)
(0,0)
(
0
,
0
)
,
(
0
,
10
)
(0,10)
(
0
,
10
)
,
(
10
,
0
)
(10,0)
(
10
,
0
)
, and
(
10
,
10
)
(10,10)
(
10
,
10
)
. Red squares of side length
2
2
2
are randomly placed on top of the grid, changing the color of a
2
×
2
2\times2
2
×
2
square section red. Each red square when placed lies completely within the blue square, and each square's four corners take on integral coordinates. In addition, randomly placed red squares may overlap, keeping overlapped regions red. Compute the expected value of the number of red squares necessary to turn the entire blue square red, rounded to the nearest integer. Your score will be given by
⌊
25
min
{
(
A
C
)
2
,
(
C
A
)
2
}
⌋
\lfloor25\min\{(\tfrac{A}{C})^2,(\tfrac{C}{A})^2\}\rfloor
⌊
25
min
{(
C
A
)
2
,
(
A
C
)
2
}⌋
, where
A
A
A
is your answer and
C
C
C
is the actual answer.
2015
Guts Test