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Four natural numbers of ABCD multiplied by four are equal to DCBA. What are the ABCD numbers
ABCD=1000A+100B+10C+D
4ABCD=4000A+400B+40C+4D=1000D+100C+10B+A
3999A+390B-60C-996D=0
1333A+130B-20C-332D=0
Now let's pay attention to a problem, a d * 4, so 12345689 (why not 0, because 0 can't be the first) = 4 8 2 6 0 4 2 6
A can't be equal to 0, so a can only be one of 2 4 6 8
If we look at * 4 times or 4 digits, then the number one * 4 can't exceed 10, then a can only be 2
Then d * 4 = if each digit is 2, then D may be 3 8
If we look at the above inference, a = 2, then D can only be 8
Let's pay attention to another question. What does a = 2 * 4 = 8 mean
It shows that B * 4 will not cause carry, that is, if B * 4 does not exceed 10, then B can be 0 1 2
Now, let's substitute these two definite values a and D into the previous equation
1333A+130B-20C-332D=1333*2+130B-20C-332*8=10+130B-20C=0
Now we substitute B in when B = 0 and C = 0.5 is not an integer error
When B = 1, C = 7 is satisfied
C = 13.5 is not an integer error when B = 2
So ABCD is 2 1 7 8
2178*4=8712
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