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.

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?

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 non-zero 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.

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.