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Omni-MATH / On a blackboard a stranger writes the values of s₇(n)² for n=0,1,…,7²⁰−1, where s₇(n) denotes the sum of digits of n in base 7 . Compute the average value of all the numbers on the…

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problem

On a blackboard a stranger writes the values of s7(n)2s_{7}(n)^{2} for n=0,1,…,720−1n=0,1, \ldots, 7^{20}-1, where s7(n)s_{7}(n) denotes the sum of digits of nn in base 7 . Compute the average value of all the numbers on the board.
Plain-text mathematical notation (without MathML)
On a blackboard a stranger writes the values of s₇(n)² for n=0,1,…,7²⁰−1, where s₇(n) denotes the sum of digits of n in base 7 . Compute the average value of all the numbers on the board.
Original LaTeX notation
On a blackboard a stranger writes the values of $s_{7}(n)^{2}$ for $n=0,1, \ldots, 7^{20}-1$, where $s_{7}(n)$ denotes the sum of digits of $n$ in base 7 . Compute the average value of all the numbers on the board.

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Source and history

task_id
5c4da1b2-4e2a-573f-9de1-808e31ad3c7c
task_key
test--5c4da1b2-4e2a-573f-9de1-808e31ad3c7c
task_revision_id
1
config / split
/ test

Official source

initial import