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

1 Answer
Aug 10, 2017

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