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Problem 463

AMC 12 late, AIME early

Number theory Difficulty 4.8 Find the answer

Task 2. Let $f(n)$ be equal to the product of the even digits of the natural number $\mathrm{n}$ or be equal to zero if there are no even digits. Find the sum $f(1)+f(2)+\cdots+f(100)$ .

This one wants a proof. Work it on paper, read the official solution, then mark yourself honestly — the ladder only means something if the record is true.

Official solution

Task 2. Let $f(n)$ be equal to the product of the even digits of the natural number $\mathrm{n}$ or be equal to zero if there are no even digits. Find the sum $f(1)+f(2)+\cdots+f(100)$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.