Question 1203026
<br>
This problem can of course be solved by trial and error; but solving the problem using logical reasoning is a good mental exercise.<br><pre>
  7 4 2 5 8 6
+ 8 2 9 4 3 0
-------------
1 2 1 2 0 1 6</pre>
The addition is correct for the final three digits:<br><pre>
  5 8 6
+ 4 3 0
-------
  0 1 6</pre>
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.<br>
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.<br>
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.<br>
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.<br>
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.<br><pre>
  7 4 6 5 8 6
+ 8 6 9 4 3 0
-------------
1 6 1 6 0 1 6</pre>
ANSWER: d+e = 2+6 = 8<br>