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2022 BMT
26
26
Part of
2022 BMT
Problems
(1)
BMT 2022 Guts #26
Source:
8/31/2023
Compute the number of positive integers
n
n
n
less than
1
0
8
10^8
1
0
8
such that at least two of the last five digits of
⌊
1000
25
n
2
+
50
9
n
+
2022
⌋
\lfloor 1000\sqrt{25n^2 + \frac{50}{9}n + 2022}\rfloor
⌊
1000
25
n
2
+
9
50
n
+
2022
⌋
are
6
6
6
. If your submitted estimate is a positive number
E
E
E
and the true value is
A
A
A
, then your score is given by
max
(
0
,
⌊
25
min
(
E
A
,
A
E
)
7
⌋
)
\max \left(0, \left\lfloor 25 \min \left( \frac{E}{A}, \frac{A}{E}\right)^7\right\rfloor \right)
max
(
0
,
⌊
25
min
(
A
E
,
E
A
)
7
⌋
)
.
number theory