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5
2016 Combo #5
2016 Combo #5
Source:
December 30, 2016
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
,
d
d
d
,
e
e
e
,
f
f
f
be integers selected from the set
{
1
,
2
,
…
,
100
}
\{1,2,\dots,100\}
{
1
,
2
,
…
,
100
}
, uniformly and at random with replacement. Set
M
=
a
+
2
b
+
4
c
+
8
d
+
16
e
+
32
f
.
M = a + 2b + 4c + 8d + 16e + 32f.
M
=
a
+
2
b
+
4
c
+
8
d
+
16
e
+
32
f
.
What is the expected value of the remainder when
M
M
M
is divided by
64
64
64
?
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