Question

4x(ABCD)=DCBA what is ABCD ?

Answer 1

`ABCD=2178`

Explanation:

If `A`, `B`, `C`, `D` are digits of a `4` digit number, then we can reason as follows:

Given:

`4ABCD = DCBA`

• `A` is `1` or `2`, since otherwise `4ABCD` would run to `5` digits.

• `A` is even since it's the last digit of `4ABCD`, so that means it must be `2`.

• `D >= 8` and hence `D=8` or `9`.

• Since the last digit of `4D` is `A`, we can deduce that `D=8`.

• So there are no carries into the `1000`'s and there is a carry of `3` into the `10`'s. So `4BC+3 = CB`

• Hence `B` is odd and `1` or `2`, so must be `1`.

• Then the last digit of `4BC+3` is `1`, so the last digit of `4BC` is `8` and `C=2` or `C=7`. Hence `C=7`

`ABCD=2178`

Answer 2

If `ABCD` AND `DCBA` were intended to be 4-digit numbers (with `A, B, C, and D` representing single digits:
`color(white)("XXX")ABCD=2178`

Explanation:

`4xx2178=8712`

(only non-zero combination that I was able to find)

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