How many 6 digits can be formed puzzle

How many six digit numbers can be formed using the digits 1 to 6, without repetition such that the number is divisible by the digit at its unit place?

6 digot numbe puzzle

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SherlockHolmes Expert Asked on 25th February 2016 in Math Puzzles.
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  • 1 Answer(s)
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    Answer- 648

    Explanation-
    XXXXX1 is always divisible by 1, so we have 5! numbers.
    XXXXX2 is always divisible by 2, so we have 5! numbers.
    XXXXX3 is always divisible by 3 (sum of digits is always 21), so we have 5! numbers.
    XXXXY4 is divisible by 4 only if Y is 2 or 6, so we have 2 * 4! numbers.
    XXXXX5 is always divisible by 5, so we have 5! numbers.
    XXXXX6 is always divisible by 6 (even number divisible by 3), so we have 5! numbers.

    So total number of numbers with required property = 5 * 5! + 2* 4! = 600 + 48 = 648 numbers.

    Detective Expert Answered on 27th February 2016.
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