Combinatorics · Counting · Divisibility rules · Digit problems

Problem 1, 1998

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How many three-digit numbers written using the digits \(0, 1, 2, 3, 4, 5\) are divisible by \(15\), if

(a) all digits must be distinct? (b) digits may repeat?

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Serbian Municipal Competition 1998, high school grade I, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source