The total number of three-digit numbers, with one digit repeated exactly two times, is\_\_\_
Answer: 243
Solutions · 1
Official solution
Case 1: All digits non-zero. Choose the repeated digit and the distinct digit: (19)×(18) ways to pick digits, times 2!3!=3 arrangements: 9×8×3/... --- following the source's grouping: (29)×2×23!=216
Case 2: One digit is 0.
- Pattern 0,0,x (0 repeated, but 0 can't be leading): 9×1=9
- Pattern 0,x,x (x repeated, x=0): 9×2=18
\[\text{Total} = 216+9+18 = 243\]