A, B, C, and D are digits which are all less than 9 and are not necessarily distinct. What is the sum of all the elements of all ordered 4-tuples (A,B,C,D) such that 0.AB⎯⎯⎯⎯⎯⎯⎯‾‾‾‾‾√=0.CD⎯⎯⎯⎯⎯⎯⎯⎯ where 0.AB⎯⎯⎯⎯⎯⎯⎯ represents the repeating decimal 0.ABABAB… and similarly for 0.CD⎯⎯⎯⎯⎯⎯⎯⎯?

Guest Feb 25, 2020

edited by
Guest
Feb 25, 2020