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2016 ASDAN Math Tournament
27
27
Part of
2016 ASDAN Math Tournament
Problems
(1)
2016 Guts #27
Source:
8/14/2022
Suppose that you are standing in the middle of a
100
100
100
meter long bridge. You take a random sequence of steps either
1
1
1
meter forward or
1
1
1
meter backwards each iteration. At each step, if you are currently at meter
n
n
n
, you have a
n
100
\tfrac{n}{100}
100
n
probability of
1
1
1
meter forward, to meter
n
+
1
n+1
n
+
1
, and a
100
−
n
100
\tfrac{100-n}{100}
100
100
−
n
of going
1
1
1
meter backward, to meter
n
−
1
n-1
n
−
1
. What is the expected value of the number of steps it takes for you to step off the bridge (i.e., to get to meter
0
0
0
or
100
100
100
)?Let
C
C
C
be the actual answer and
A
A
A
be the answer you will submit. Your score will be given by
max
{
0
,
⌈
25
−
25
∣
log
6
(
A
−
C
/
2
C
/
2
)
∣
0.8
⌉
}
\max\{0,\lceil25-25|\log_6(\tfrac{A-C/2}{C/2})|^{0.8}\rceil\}
max
{
0
,
⌈
25
−
25∣
lo
g
6
(
C
/2
A
−
C
/2
)
∣
0.8
⌉}
.
2016
Guts Round