[furyshade]

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I just had a solution written out but somehow it erased .

In any case , I figured out that if the 10 digit integer is abcdefghij then it turns out that the solutions are

a+f=9 , b+g=9 , c+h=9 , d+i=9 , e+j=9 as long as we take into account that the first digit cannot be a 0 .

So a solution may be 4321056789 or 5678943210 ...
It's relatively easy to count the total number of solutions given the constraints .

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unless im doing something wrong it seems the answer is 10 nPr 10, or 3628800