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MathNet 2015-part-02 — 191 problems (EN–VI) Question 145

Math Olympiad Vault · MathNet 2015-part-02 — 191 problems (EN–VI)

Question 145

Is there a two-digit number $n$ that does not end with zero such that

a) all numbers that can be formed by adding one or more zeros between the two-digit number's digits are its multiples?

b) none of the numbers that can be formed by adding one or more zeros between the two-digit number's digits are its multiples?

c) some numbers that can be formed by adding one or more zeros between the two-digit number's digits are its multiples and some are not?