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7
2017 Theme #7
2017 Theme #7
Source:
May 8, 2018
combinatorics
Problem Statement
On a blackboard a stranger writes the values of
s
7
(
n
)
2
s_7(n)^2
s
7
(
n
)
2
for
n
=
0
,
1
,
.
.
.
,
7
20
−
1
n=0,1,...,7^{20}-1
n
=
0
,
1
,
...
,
7
20
−
1
, where
s
7
(
n
)
s_7(n)
s
7
(
n
)
denotes the sum of digits of
n
n
n
in base
7
7
7
. Compute the average value of all the numbers on the board.
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