Permutations and Combinations Part 1

∵x∈[100,999],x∈N
Then ‌

x

2

∈[50,499],‌

x

2

∈N
Number whose G.C.D. with 18 is 1 in this range have the required condition. There are 6 such number from 18 ×3 to 18×4. Similarly from 18×4 to 18×5......,26×18 to 27×18
∴ Total numbers =24×6+6=150
The extra numbers are 53,487,491,493,497 and 499.