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<h1 class="puzTitle">Marther's Vineyard Puzzle - Solution</h1><div class="puzPuzzle"><h2>The Puzzle:</h2><div class="puzText"><div class="puzThumb"><a href="sam-loyd-puzzles-index.html"><img src="images/marthers-vineyard.jpg" width="350" height="267" alt="Marther's Vineyard" style="border-style: none" /></a></div>What are the maximum number of grape vines that can be planted, not closer than nine feet apart, in a square plot containing one-sixteenth of an acre? <br />
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(Note: each side of this square plot would be 52 feet 2 inches)</div></div><div class="puzSep"></div><div class="puzSoln"><h2>Our Solution:</h3><div class="puzSolnText">By drawing a line on the bias as shown in the adjoining diagram, from one corner to another, and crossing and paralleling the same, it will be found that 41 vines can be planted, a little over nine feet apart, and well within the fence line.<br />
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<img src="images/marthers-vineyard-solution.jpg" /><br />
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HOWEVER, Peter Noll has found a better solution: 44 grape trees <br />
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This comes about by planting 6,5,6,5,6,5,6,5 trees in 8 layers with horizontal spacing 10.433 feet and layer distances 7.45 feet. Any 3 adjacent trees form a triangle with side lengths 10.433, 9.097, 9.097 feet.<br />
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<img src="images/marthers-vineyard-solution-noll.gif" /></div></div><div class="puzAuthor">Puzzle Author: Loyd, Sam<br /><br /></div><div class="puzSolnFtr">See this puzzle <a href="marther-s-vineyard.html">without solution</a><br />Discuss this puzzle at the <a href="http://www.mathisfunforum.com/index.php">Math is Fun Forum</a></div><div class="related"><a href="sam-loyd-puzzles-index.html">Sam Loyd Puzzles</a><a href="index.html">Puzzles Index</a></div><!-- #EndEditable --></div>
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