Prove or disprove the following:
For any integer number N there exists at least one integer number M, such that the decimal presentation of M*N needs only two distinct digits.

(In reply to re(2): possible solution by broll)

1.".I assumed that 'only two distinct digits' meant exactly two for "..

AND RIGHTLY SO.

 Anyone with common sense would object to describing 0 (zero)
as two-distinct-digit number.
When anyone asks you "tea or coffee?" only professional nitpicker might respond with a clarifying question
"Is the or inclusive or exclusive?"

2. Re your remark - d3 or d4 - I felt like 3.5 and was about to comply with your suggestion, but apparently was too slow.
No big deal.

3. I missed the "Jim" part - please explain...

Posted by Ady TZIDON on 2015-01-18 04:18:04