Maximum numbers that can be formed using all the 4 digits 6, 4, 8, 1 without…

Key idea: Divisibility by 9 depends only on the sum of the digits.

Sum of the given digits: 6 + 4 + 8 + 1 = 19, which is not divisible by 9.

Because rearranging digits does not change their sum, no permutation of these four digits can produce a number divisible by 9.

• We must use all four digits without repetition, so only 4-digit numbers are considered.

• Since the digit-sum 19 is not a multiple of 9, there are 0 such numbers.