Question 1110788
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Eliminating redundant information, and keeping all the comparisons of the digits "going in the same direction", we can re-state the problem like this:
the 1st digit is 2 more than the 2nd
the 2nd digit is 2 more than the 3rd
the 3rd digit is 2 more than the 4th
the 4th digit is 1 more than the 5th<br>
So the 1st digit is the largest of the first five digits, and probably the largest of all the digits.<br>
Now you could probably finish solving the problem using formal algebra; but it seems logical reasoning will get you to the answer faster.<br>
So let's see what happens if we let the first digit be the largest it can be: 9.  Then the 6-digit number is 97532x; and since the sum of all 6 digits is 30, the 6-digit number would be 975324.<br>
And that number satisfies the remaining condition of the problem -- the sum of the first four digits is 24, and the last two digits are 24.  So<br>
Answer: the 6-digit number is 975324.