Here's another hidden number problem to play with. I have a secret number (positive integer) N. N is not a multiple of 10. I tell you the sum of the digits, and perhaps an upper bound. You give me a multiplier M1. I tell you the digit sum of M1*N. You give me M2, I tell you the digit sum of M2*N. Etc. Eventually, you guess the number. Puzzles: Can you determine a unique N? Is there a better strategy than just using 2,3,4,... for Mi? For ten-digit N, a program can run through all the possibilities consistent with the current state-of-play. But What if N is twenty or thirty digits? Is there some non-enumerative algorithm that's more efficient for finding N? Extra credit: N^Mi instead of Mi*N. I've had some ideas about this puzzle, but nothing I'd call a solution. Rich