Daycounter,
Inc. Engineering Services 


The sum of the digits of N*9 is 9,Where 0<N<10 Example: 2*9 = 18, the sum of the digits is 9 3*9= 27, the sum of the digits is 9, etc. Proof: Define sumdig(I2) as the sum of the digits of a 2 or 1 digit integer number I2. Note that a 2 digit number can be expressed as I2= 10*N2 + 1*N1 (Definition 1). where N1 and N2 are an integer 0<N1,N2<10. Therefore: sumdig(10*N2+1*N1) = N2+N1. (Equation 1). We must show that: sumdig(N*9)= 9 where 0<N<10. sumdig(N*9)= sumdig(N*(109))= sumdig(10NN)= sumdig((10N10) + (10 9N)) = sumdig( 10*(N1) + (10 N)) (Equation 2). Since 0<N<10, then 0<= N1<9, Equation 2 fits the form of Definition 1, where (N1) is N2 and (10N) is N1. sumdig( 10*(N1) + (10 N)) = N1+ 10N = 9 QED.
Daycounter specializes in contract electronics design. Do you need some help on your project? Contact us to get a quote.
[Employment] [Downloads] [Articles] [Contact Us] Salt Lake City, UT, USA
Disclaimer: Daycounter, Inc. doesn't guarantee the accuracy of any of it's content. Use at your own risk.
