## Round 4: Problem 1

Alice’s brother Bob won a math contest in 2007 by writing 2007 as a sum of positive integers that together used each of the digits 0, 1, 2,…, 9 exactly once. Bob’s sum was 2007 = 1907 + 84 + 2 + 3 + 5 + 6. Alice wants to prepare for the final round of the 2009 CUNY Math Challenge by writing 2009 as a sum of positive integers that together use each of the digits 0, 1, 2,…, 9 exactly once. Either give a sum of numbers that Alice could use, or prove that there is no such sum. (Of course, no positive integer can begin with the digit 0.)

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=_= How come all questions of this round are prove problem???

Utin pApril 22, 2009 at 17:53

Since the sum of the digits 2+0+0+9 differs mod 3 from the sum of the digits 0 through 9, there is no solution.

jimApril 27, 2009 at 07:49