Four. Doing N tries with 10 marbles is equivalent to doing a single trial with 10 N-digit binary numbers (the i^th digit of the j^th number is 1 if on the i^th trial the j^th ball is white). Three is therefore insufficient as there will be at least two identical numbers, but it's easy to produce 10 distinct inputs with N=4 (noting that for each j exactly 5 of the numbers must have a 1 in the j^th digit), e.g. 0000 0001 0011 0110 0101 1001 1010 1100 1110 1111 J.P. On 4/17/07, David Wilson <davidwwilson@comcast.net> wrote:

Suppose you have a box with a hole on the top and the side. When you feed 10 marbles into the top hole, a mechanism in the box shuffles the marbles and sends them out in a specific permuted order. If you have 5 identical white and 5 identical black marbles, how many tries are necessary to determine the permutation? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun