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The rightmost non-zero digit in


\( \begin{align*} &(1001001)(1010101)+(989899)(1001001)\\ &\qquad -(1001)(989899)-(1010101)(1001) \end{align*}\)


is  a, and it is followed by b zeroes. Find the ordered pair (a,b)

 Apr 22, 2018
edited by gueesstt  Apr 22, 2018

Hey! I'm back,


So, if you look at \((1001001)(1010101)+(989899)(1001001)\),


You can see that both share a commom 1001001


This means we can factor out the 1001001:

\(1001001(1010101+989899) \)


You can easily tell the number in the paranthesis is 2000000.


The same goes with\( -(1001)(989899)-(1010101)(1001)\)


We can factor out the -1001:




Once againg, we have very easy numbers we can do in our head:




Combining those two expressions, we have:


\( 1001001(2000000)-1001(2000000)\)


Once again, we can factor out the 2000000




Finalizing, we have:




The number we are looking for is 2000000000000, or 2 trillion.


So a, is 2, and b is 12


The ordered pair is (2,12)

 Apr 22, 2018

Thank you!

gueesstt  Apr 22, 2018

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