I will try to solve this problem in least number of complex mathematical steps possible. I will not use any maths greater than grade 8. ABCD*4 = DCBA implies A must be less than 3 since A is at 1000s place and 3*4 = 12, which makes the given number a five digit number. Thus A can be 1 or 2. Since DCBA is a multiple of 4 it implies that A must be even and hence A is 2. A is 2 again implies D must be 8 or 9. (D cannot be less than 8 since it is at the 1000s place of DCBA, which