The Crazy Number

Logic Level 3

If there is a special nine - digit - number A B C D E F G H I 'ABCDEFGHI' where A , B , C , D , E , F , G , H , I A,B,C,D,E,F,G,H,I are distinct digits.

If the number formed by first

  • one digit ('A') is divisible by 1

  • two digits ('AB') is divisible by 2

  • three digits ('ABC') is divisible by 3

  • first four digits ('ABCD') is divisible by 4

  • and so on till 9 ...

Then find the nine - digit - number


The answer is 381654729.

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1 solution

We have the following constraints:

(i) The digit B B must be even

(ii) A + B + C A+B+C must be divisible by 3 3

(iii) C D \overline {CD} must be divisible by 4 4

(iv) E E must be 5 5

(v) F F must be even and D + E + F D+E+F must be divisible by 3 3

(vi) A + G D + 2 ( E B ) + 3 ( F C ) A+G-D+2(E-B)+3(F-C) must be divisible by 7 7

(vii) F G H \overline {FGH} must be divisible by 8 8

Using all these, we get the number A B C D E F G H I 381654729 \overline {ABCDEFGHI}\equiv \boxed {381654729} .

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