For a positive base ten integer of the form ABCD drawn at random between 1111 and 9999 inclusively, determine the probability that ABCD is divisible by each of AB, AC, AD, BD and CD; but, not divisible by BC.

Note: Each of the letters in bold represents a digit from 1 to 9, whether same or different.

(In reply to ABACADABrA (Solution) by Jer)

To take one example, 1995 is divisible by 95, not because 19 is divisible by 95, but rather because 19 is one of the factors of 95 and 100 is divisible by the other factor.

Posted by Charlie on 2010-10-19 19:12:46