Inverted nine

In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?

Result

n =  18

Solution:

n1=114 n2=714 n3=414 n4=174 n5=774 n6=474 n7=894 n8=144 n9=744 n10=444 n11=984 n12=918 n13=978 n14=198 n15=798 n16=498 n17=948 n18=888 n=18n_{1}=114 \ \\ n_{2}=714 \ \\ n_{3}=414 \ \\ n_{4}=174 \ \\ n_{5}=774 \ \\ n_{6}=474 \ \\ n_{7}=894 \ \\ n_{8}=144 \ \\ n_{9}=744 \ \\ n_{10}=444 \ \\ n_{11}=984 \ \\ n_{12}=918 \ \\ n_{13}=978 \ \\ n_{14}=198 \ \\ n_{15}=798 \ \\ n_{16}=498 \ \\ n_{17}=948 \ \\ n_{18}=888 \ \\ n=18

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