Can you find all of the totals between 700 and 800 that can be made by a number plus its reversal?
This is my method:
The hundreds digit has to be 7, this is due to the total being between 700 and 800.
The tens digit can be any even number. I know this because when you reverse a 3-digit number, the tens column doesn’t change, so adding a 3-digit number to its reverse always makes the total of the tens digit double the original digit in the tens column, making that total EVEN.
The units digit also has to be 7. This is because when you add a 3-digit number to its reverse, you can represent this as
ABC
+CBA
DED where 2B=E, and A+C=D. As you notice, the hundreds digit equals the ones digit in this sum (of course the values are different). In this case, our hundreds digit= our ones digit=7.