October 16–October 22, 2007
Problem
Suppose raffle tickets are identified by a six-digit number. A ticket (number) is lucky if the sum of the first three digits is equal to the sum of the last three digits. For example, the number 254119 is lucky since 2 + 5 + 4 = 1 + 1 + 9. Show that if you add up all the possible lucky ticket numbers, the sum is divisible by the unlucky number 13.
Marios Pavlides suggested the following extension if you want a bigger challenge: actually find the sum S of the lucky numbers, and find the largest prime factor of S. (This part is optional; it has no impact on ice-cream eligibility!)
Solution
here.
List of solvers
Aaron Dilley, Bob Sterling, Michelle Kim (undergraduate); Field Cady, Dustin Moody, Robert Bradshaw, Adam Estrup, Peizhe Shi, Aneesh Hariharan (graduate); Gary Raymond, Marina Meila (faculty); Rich Bauer (alum)
Aaron Dilley wins the prize!