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 re: ABACADABrA (Solution) by Charlie)

Charlie: I used essentially the same program logic, and came to the same results (and probability) as you.  After posting, I was puzzled when I read Jer's approach.  Possibly he was reading the puzzle as reference to products (e.g. ABCD = A*B*C*D; AB=A*B, etc.) rather than as an alphameric of sorts, where each letter stands for a digit within a 2- or 4-digit number.  The final "Note" could perhaps be read either way, but for me the references to 1111 and 9999 clearly favored considering these as 4-digit numbers, not as products.

Posted by ed bottemiller on 2010-10-19 20:04:51