In Computer Science feed, if you come across A+B+C+D+E=15 and then asked to find the value of F+G+H+I+J , then one of the approaches is 1+2+3+4+5=15A+B+C+D+E=15 and then you assign the numbers F,G,H,I,J their respective numbers from position in Alphabets, giving 6+7+8+9+10=40F+G+H+I+J=40
But if you do that in Maths , for some unknown positive integersA,B,C,D,E,F,G,H,I,J ,
A+B+C+D+E=15⟹F+G+H+I+J=40
then it is a Big Mistake !!! (You can't say 1st equation implies the 2nd)
But for how many ordered 10-tuples of distinct positive integers (A,B,C,D,E,F,G,H,I,J), are the above two equations simultaneously true ?
Details and assumptions :-
∙ All the alphabets A,B,C,D,E,F,G,H,I,J are distinct and are some positive integers.
∙ The tuple (1,2,3,4,5,6,7,8,9,10) is different from (2,1,3,4,5,6,7,8,9,10).