Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1,2,3,4,5 with repetition, is \_\_\_\_\_\_\_\_\_.
Answer: 16
Solutions · 1
Official solution
A number is divisible by 6 if it is divisible by both 2 and 3. A number is divisible by 2 if its last digit is even, which means it must be either 2 or 4 from the given digits. A number is divisible by 3 if the sum of its digits is divisible by 3.
(2,1,3),(2,3,4),(2,5,5),(2,2,5),(2,2,2)(4,1,1),(4,4,1),(4,4,4),(4,3,5)2,1,3⇒312,1322,3,4⇒342,432,234,3242,5,5⇒5522,2,5⇒252,5222,2,2⇒2224,1,1⇒1144,4,1⇒414,1444,4,4⇒4444,3,5⇒354,534
Total 16 numbers.