16 Dec
2011
16 Dec
'11
10:35 a.m.
I give you an arbitrary positive integer x > 0.
You write down x, 2x, 3x, 4x, ..., kx in decimal.
How large much k be to guarantee that every digit appears somewhere in your list, regardless of x?
What is the smallest k for which there are k positive integers m_1 , m_2 , ... , m_k such that, for every positive integer x , all ten decimal digits occur on the list m_1 x , m_2 x , ... , m_k x ? (The solution of the original problem shows that such k exist.) Michael Reid