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.)

vwxy is either 7531 or 9753. If vwxy=7531, then 9 must be in either pqr or stu. It cannot be in stu because stu has all even digits. Therefore, 9 is in pqr, so the other two digits in pqr are both 0. That is a contradiction since there is only one 0. Therefore, vwxy=9753. That means that 1 is either in pqr or stu. It has to be in pqr because stu has all even digits. The other two digits in pqr have to add up to 8, and they are both even. They cannot both be 4, so they are either 2 and 6, or 0 and 8. If they are 2 and 6, then stu cannot be consecutive even digits. Therefore, they are 0 and 8, so p=810.

Posted by Math Man on 2011-09-28 11:31:30