Presented by Cold Stone Creamery(R)

The Department of Mathematics Challenge of the Week

Solution to Challenge 4, Fall '04

Let n be a positive integer. Consider the first n+1 integers in the sequence (7, 77, 777, 7777, ..., ). Each of these n+1 numbers has only n possible remainders when divide by n, so two of them must have the same remainder by the pigeonhole principle. The difference of these two is a jackpot and divisible by n.

Correct solutions: Bob Liebler, Ben Manvel (faculty), Florian Hulpke (University of Hannover), Byungsoo Kim (Seoul), Julien Gaigneur (Cellzome Corp., Heidelberg)


Previous Challenges, Fall '04

Challenge 1

Challenge 2

Challenge 3


If you would like to receive a weekly email reminder about the Challenge Problem, send an email to solution@math.colostate.edu

The Department of Mathematics Challenge Problem is sponsored by the Cold Stone Creamery, which is providing all the prizes.

If more than one correct solution is submitted, one prize winner will be chosen from among the correct solutions. Submissions from CSU faculty and people not affiliated with CSU are encouraged, but they are ineligible for the prizes.

For questions, comments or suggestions for future challenge problems: please e-mail Ross McConnell, rmm@cs.colostate.edu.