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#