document.write( "Question 1110788: Find the six-digit number in which the first digit is 2 more than the second, the second digit is 2 more than the third, the third is 2 less than the second, the fourth is 2 less than the third, the fifth is 1 less than the fourth, and the last two digits are the sum of the first four. The sum of all six digits is 30. \n" ); document.write( "

Algebra.Com's Answer #725791 by greenestamps(13215) $\"\"$ $\"About$

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\n" ); document.write( "Eliminating redundant information, and keeping all the comparisons of the digits \"going in the same direction\", we can re-state the problem like this:
\n" ); document.write( "the 1st digit is 2 more than the 2nd
\n" ); document.write( "the 2nd digit is 2 more than the 3rd
\n" ); document.write( "the 3rd digit is 2 more than the 4th
\n" ); document.write( "the 4th digit is 1 more than the 5th

\n" ); document.write( "So the 1st digit is the largest of the first five digits, and probably the largest of all the digits.

\n" ); document.write( "Now you could probably finish solving the problem using formal algebra; but it seems logical reasoning will get you to the answer faster.

\n" ); document.write( "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.

\n" ); document.write( "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

\n" ); document.write( "Answer: the 6-digit number is 975324. \n" ); document.write( "

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