document.write( "Question 1203026: The addition below is incorrect. The display can be made correct by changing one digit d, wherever
\n" ); document.write( "it occurs, to another digit e. Find the sum of d and e.
\n" ); document.write( " 742586
\n" ); document.write( "+ 829430
\n" ); document.write( "= 1212016
\n" ); document.write( "Please help me solve this problem \n" ); document.write( "
Algebra.Com's Answer #838244 by greenestamps(13198)\"\" \"About 
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\n" ); document.write( "This problem can of course be solved by trial and error; but solving the problem using logical reasoning is a good mental exercise.
\r\n" );
document.write( "  7 4 2 5 8 6\r\n" );
document.write( "+ 8 2 9 4 3 0\r\n" );
document.write( "-------------\r\n" );
document.write( "1 2 1 2 0 1 6

\n" ); document.write( "The addition is correct for the final three digits:
\r\n" );
document.write( "  5 8 6\r\n" );
document.write( "+ 4 3 0\r\n" );
document.write( "-------\r\n" );
document.write( "  0 1 6

\n" ); document.write( "So it is unlikely that any of the digits in that part of the problem -- 0, 1, 3, 4, 5, 6, and 8 -- is the one that changes. So very probably the digit that changes is 2, 7, or 9.

\n" ); document.write( "In the thousands column we have digits 2 and 9 in the addends, plus a carry, yielding digit 2 in the sum. So the 9 can't change; however, the digit 2 can change to any other digit and the addition in the thousands column will still be correct.

\n" ); document.write( "In the ten thousands column, we have digits 4 and 2 in the addends yielding digit 1 in the sum. We don't want the 1 or 4 to change, so the 2 MUST change.

\n" ); document.write( "There is a carry from the thousands column to the ten thousands column, so the 2 must change to a 6 to make the addition correct in the ten thousands column.

\n" ); document.write( "So it appears changing digit 2 to digit 6 is what we need to do. And doing that shows that the addition is now correct.
\r\n" );
document.write( "  7 4 6 5 8 6\r\n" );
document.write( "+ 8 6 9 4 3 0\r\n" );
document.write( "-------------\r\n" );
document.write( "1 6 1 6 0 1 6

\n" ); document.write( "ANSWER: d+e = 2+6 = 8

\n" ); document.write( " \n" ); document.write( "
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