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6874 has the same digit sum as 6775 because 6874 = 6874 – 99. In fact, they have the same digit difference because the difference is a multiple of 11.
And if you have a decimal point, it’s
E O E O . E O E O
I came here to ask this exact question, so I’m glad I looked at previous replies first.
Is there an easier way of doing this? The more digits I want to square, the harder this task will get. For example, if I want to square 12345, then I don’t want to be doing 1234 * 1235 at first. What do you think?
This makes sense because 10 * 10 = 100, and the DD of 100 = 1 = 1 * 1.
Still, sometimes I have to add 11 to the final answer, such as when I multiply 21 by 58. The DD method would show 3, which is the same as 8, which is the same as the DD method for the answer, 1218.
Actually, I came up with one. I multiplied 35 * 67 and got 2455 instead of 2345, and I knew it was wrong only because of the DS method.
So the DS method will fail where the DD method succeeds when the correct answer is added to a nonzero multiple of 11 that is not a also a multiple of 9. So coming up with 3335 would have made the DS and DD methods both succeed, but the answer would have been wrong.
But I do have a question myself. Where would the DS method catch something that the DD method wouldn’t? The lecture videos didn’t say in that section.
The DD method will catch decimal point placement and number transposition errors. For example, as the videos say, if you write 16.1 / 7 = 23, then the DD method will produce 1 instead of 10, while the DS method won’t catch it. Then, if you write 242 instead of 224, the DS method will provide the same answer for each, while the DD method won’t.

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