Consider a pair of 3-digit numbers 122 & 213.
Their product is 25986.
Invert both numbers and consider the new product- it is 68952 i.e. inversion of the previous result!

List all such pairs of 3 digit numbers, avoiding trivial solutions.

Are there such pairs of 4 digit numbers?

Either find some or prove there are none.

Any pair of numbers that avoids carries when adding the partial products will do.

           1112
         X 2113

           3336
          1112
         1112
        2224

        2349656     

 Extra credit:

Here are some of the non-trivial 7 digit numbers that work
1111112 X 1111121 = 1234579876552
2111111 x 1211111 = 2556789754321

Posted by Steve Herman on 2022-01-05 07:58:24