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Start with a two-digit number, reverse digits to make a new number then subtract the smaller from the larger number...

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Start with a two-digit number, reverse the digits to make a new number then subtract the smaller from the larger number. Repeat this process until you reach a single digit. Start with other numbers. What do you notice, answer with the explanation why is it happening.

posted Nov 28, 2017 by anonymous

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Let any 2 digit number be (10×a + b) then on reversing the digit's places we get (10×b + a). Now subtracting the 2 gets us
(9×a - 9×b) = 9(a-b). Therefore for any 2 digit number the following steps always yields a number which is either 9 or it's multiples and when continued gives 9 as the answer in one of its steps.

answer Nov 28, 2017 by Tejas Naik



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