Question

Find the four digit number ABCD such that ABCD multiply 4=DCBA?

Answer 1

`ABCD = 2178`

Explanation:

I found a partial solution in a Math Forum .

The forum says that `A =2`, because anything greater would cause a carry and anything less would make the product odd.

`2BCD`
`ul(xxcolor(white)("...")4)`
`DCB2`

The forum says that `D = 8`, because that will give us the 2 and the 8 in the product:

`2BC8`
`ul(xxcolor(white)("..")4)`
`8CB2`

The forum says that `B=1`, because there is no carry into the 4th column, 2 is already used and it cannot be 0:

`21C8`
`ul(xxcolor(white)(".")4)`
`8C12`

The forum leaves us to figure out what C is.

We know that there is 3 carried into that column so `4xxC` must end in 8; C must equal 7: `4xx7= 28`

`2178`
`ul(xx4)`
`8712`