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.
I wondered if abc*cde is a such a pair then abc*edc would be as well. Usually it works, but there are exceptions.
211*411=86721
112*114=12768
but
211*114=24054
112*411=46032
(the partial products are different and now have a carry.)
I wonder if there is a very large example with many digits whose partials products cause lots of carries, but the products still reverse.
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Posted by Jer
on 2022-01-05 12:14:58 |
Observation
