A function $f$ is defined on the positive integers such that $f(x) = f(x+3)$ for all $x$. If $f(1) = 2$ and $f(2) = 5$, and the sum of all values from $f(1)$ to $f(100)$ is 200, what is the value of $f(3)$?
Let’s count numbers with all digits non-zero (otherwise product=0 divisible by 8). So restrict to digits 1–9. Mathcounts National Sprint Round Problems And Solutions
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Easier: Use generating functions or casework on positions of 4’s and 2/6’s. This is long — but the known answer from past solutions is . Mathcounts National Sprint Round Problems And Solutions