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 Ducks in a row (Posted on 2003-08-04)
Given an integer n (n≠0), there are a finite number of sequences of consecutive integers whose terms add up to n (If n=25, then 3+4+5+6+7=25 is one such sequence with 5 terms).

a. Find an equation for the number of terms of the longest such sequence for any positive integer n.

b. Find equations for the bounds (the first and last terms) of the longest such sequence for any positive integer n.

Hint: Once you have an equation for the number of terms, and for the first term of the sequence, the last term is simply one less than their sum.

Hint 2: Ducks have absolutely nothing to do with the problem.

 See The Solution Submitted by DJ Rating: 4.4167 (12 votes)

 Subject Author Date My solution H 2003-08-04 16:43:28 re: Some hints Gamer 2003-08-04 15:36:13 Some hints Federico Kereki 2003-08-04 10:00:49 re: Picky of me....leads to solution? Brian Wainscott 2003-08-04 07:21:23 Picky of me.... Brian Wainscott 2003-08-04 06:59:21 re: Queue problems DJ 2003-08-04 06:45:22 Queue problems Gamer 2003-08-04 06:36:11

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