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 _____.

A 3-digit number using digits {1,2,3,4,5} with repetition, divisible by 6.

Divisible by 2: last digit must be 2 or 4.

Divisible by 3: sum of digits divisible by 3.

Residues mod 3 of {1,2,3,4,5}: 1→1, 2→2, 3→0, 4→1, 5→2. Count: 0→1, 1→2, 2→2.

Last digit = 2 (residue 2): need $$d_1 + d_2 \equiv 1 \pmod{3}$$.

Pairs: (0,1): 1×2=2, (1,0): 2×1=2, (2,2): 2×2=4. Total = 8.

Last digit = 4 (residue 1): need $$d_1 + d_2 \equiv 2 \pmod{3}$$.

Pairs: (0,2): 1×2=2, (2,0): 2×1=2, (1,1): 2×2=4. Total = 8.

Grand total = $$\mathbf{16}$$.