Another fun question from my 5th grade

a, b,c, d are different counting numbers (1,2,3,4,5,6,

abcd doens't mean a times b times c times d, it means like 1,234 if a=1,b=2,c=3,d=4

find a, b, c and d such that
abcd times d=dcba

represented like this:
abcd
 d x
dcba

remember, a, b,c, d are all different

find a, b,c, d
show all work and logic

Solutions 

The given question is a doable program.

Def pal():
    for a in range
        for b in range
            for c in range
                for d in range

    %10)

                    %10

                   

                  %10

                   

                     %10 

if (a!=b and a!=c and a!=d and b!=c and b!=d and c!=d and x==a and y==b and z==c and w==d ):
                       print("a = ", a)
                       print("b = ", b)
                       print("c = ", c)
                       print("d = ", d)

 

Plug in the numbers to solve the problem.

The 'int' function is the same thing as floor.
The % symbol is the modulo operator

≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡

In base 10 expanded form 
and  , where A,B,C,D are counting numbers. 

We are given 
Converting to decimal expanded forms we get 

 

Distributing the above equation



brute force solution works, but is best done by a computer not by hand. 

We could also try to use modular math.