A telephone number is of the form pqr- stu- vwxy, where each letter corresponds to a different decimal digit from 0 to 9. The digit in each part are in strictly decreasing order of magnitude, that is : p > q > r, s > t > u and: v > w > x > y.

It is also known that v,w,x and y (in this order) are consecutive odd digits and s, t and u (in this order) are consecutive even digits.

Determine the 3-digit number pqr, given that p+q+r = 9, and p is not zero. (Even digits by definition will include zero digits.)

First of all that p is not zero is evident since p>q

The key to the problem is the sums of digits of each part.

vwxy is either 9753 (sum 24) or 7531 (sum 16)
stu is either 864 (sum 18) 642 (sum 12) or 420 (sum 6)

The 10 digits have a sum of 45 and since p+q+r=9 the other seven must sum to 36.

Of the above combinations the only possibility is 24 + 12
so we have pqr-642-9753 which leaves out 0, 1 and 8 so the number is

810-642-9753

Apparently this phone is in the vicinity of Salt Lake City, Utah

Edited on September 28, 2011, 11:47 am

Posted by Jer on 2011-09-28 11:12:07