Here is an attempt to solve this one without a computer.

Letting X=(abcd) in decimal notations so that its symmetric Y=(dcba)

Let us restrict to the case of no carry over for getting d so that d=Na with N>1

Then a(N^2)=a modulo 10 with the only acceptable solution N=4 and a=2 on account of the constraints (in particular N=4, a=4 excluded)

No we have to solve 4x(2bc8)=(8cb2) ie 4c+3=b modulo 10 and 4b+[(4c+3)/10]=c

Leading to c=7 and b=1 so that X=2178 and Y=8712

f unction (x)

{

as.numeric(unlist(strsplit(as.character(x),”)))

}