There were no solutions submitted from Bradley University students -- it was the week of final exams, what was I thinking! Correct solutions were received from Steve Young, Tim Kelley, CWLDOC, Aaron Kahn, Terauchi Kimio.

Let A₁,...,A₁₉₉₈ be the numbers selected, and let S_k = A₁  + ... + A_k.  If any one of the S_k is divisible by 1998, we're done.  In the contrary case, all of the S_k have a non-zero remainder when divided by 1998.  By the pigeonhole principle (there are 1998 sums but only 1997 possible remainder -- 1 to 1997) two of the sums must have the same remainder upon division by 1998.  The difference of these two sums is divisible by 1998.

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Page last updated 15 March 1999.