Question

if ABC+BCA=1341 then A+B+C=

Answer 1

ABC+BAC+CAB=ABBCC+10B+100A+C+10A+100B+B+10A+100C=C+110B+1000AABC+BAC+CAB=ABBCC+10B+100A+C+10A+100B+B+10A+100C=C+110B+1000A
and this yields to B+C=880A−100CB+C=880A−100C, and this in turn implies the number 20 divides B+CB+C. But BB and CC are digits. So 2≤B+C≤182≤B+C≤18. Clearly a contradiction.