# mowing.pdf - UCF “Practice” Local Contest — Aug 31 2019...

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Page | 9UCF “Practice” Local Contest — Aug 31, 2019Mowing Mischieffilename:mowingDifficulty Level:HardTime Limit:3 secondsBessie's younger cousins, Ella and Bella, are visiting the farm. Unfortunately, they have beencausing nothing but mischief since they arrived.In their latest scheme, they have decided to mow as much grass as they can. The farm's primegrassland is in the shape of a larget×tsquare. The bottom-left corner is (0, 0), and the top-rightcorner is (t,t). The square therefore contains (t+1)2lattice points (points with integercoordinates).Ella and Bella plan to both start at (0, 0) and run at unit speed to (t,t) while each holding one endof a very sharp and very stretchy wire. Grass in any area that is swept by this wire will be cut.Ella and Bella may take different paths, but each path consists of only upward and rightwardsteps, moving from lattice point to lattice point.Bessie is rather concerned that too much grass will be cut, so she invents a clever plan toconstrain the paths Ella and Bella take. There arenyummy flowers scattered throughout thegrassland, each on a distinct lattice point. Bessie will pick a set of

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Term
Fall
Professor
NoProfessor
Tags
Poaceae, Natural number, Lattice points