Combinatorics · Enumerative counting · Isosceles trapezoids · Parity · Floor sums · Integer solutions
How many isosceles trapezoids with integer side lengths have perimeter \(2005\)?
(A trapezoid here means a quadrilateral with exactly two parallel sides, so a parallelogram is not one. Trapezoids with the same four side lengths are counted as one.)
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Serbian Republic Competition (Republicko takmicenje) 2005, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source