Archit's Challenge 8

Logic Level 4

Find the sum of all 9-digit positive integers having all nine numbers 1 through 9 and satisfying the following conditions:

  • Sum of digits between 1 and 2 exclusive is 9.
  • Sum of digits between 2 and 3 exclusive is 18.
  • Sum of digits between 3 and 4 exclusive is 27.
  • Sum of digits between 4 and 5 exclusive is 36.

Note : For example, for the number 135792468, the sum of digits between 1 and 2 exclusive is 3 + 5 + 7 + 9 = 24 3+5+7+9=24 .


The answer is 1036737639.

Archit Agrawal by Archit Agrawal , 21, India

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1 solution

Archit Agrawal
Jan 8, 2016

the possible numbers are 472918365 and 563819274.

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Pi Han Goh - 5 years, 5 months ago

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Sum of all numbers except 4 and 5 is 36, so 4 and 5 will occupy the extreme positions. Now sum between 3 and 4 should be 27 which is only possible if 6 is adjacent to 5 and 3 is adjacent to 6. Now sum between 2 and 3 should be 18 which is only possible if 7 is adjacent to 4 and 2 is adjacent to 7. Sum between 2 and 1 should be 9 which is possible only by placing 9 between them.

Archit Agrawal - 5 years, 5 months ago

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