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112 lines
5.9 KiB
HTML
112 lines
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<div class="puzLinks"><a class="puzLink" href="measuring-puzzles-index.html">Measuring Puzzles</a><a class="puzLink" href="starter-puzzles-index.html">Starter Puzzles</a><a class="puzLink" href="../games/puzzle-games.html">Puzzle Games</a><a class="puzLink" href="logic-puzzles-index.html">Logic Puzzles</a><a class="puzLink" href="jigsaw-puzzles-index.html">Jigsaw Puzzles</a><a class="puzLink" href="number-puzzles-index.html">Number Puzzles</a><a class="puzLink" href="card-puzzles-index.html">Card Puzzles</a><a class="puzLink" href="einstein-puzzles-index.html">Einstein Puzzles</a><a class="puzLink" href="sam-loyd-puzzles-index.html">Sam Loyd Puzzles</a><a class="puzLink" href="algebra-puzzles-index.html">Algebra Puzzles</a></div> <div id="extra"></div>
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<h1 class="puzTitle">Measuring Kilograms Puzzle - Solution</h1><div class="puzPuzzle"><h2>The Puzzle:</h2><div class="puzText"><div class="puzThumb"><a href="measuring-puzzles-index.html"><img src="images/scales.jpg" width="118" height="113" alt="Measuring Kilograms" style="border-style: none" /></a></div>In front of you is a balance. <br />
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<br />
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Can you devise a system, using only 4 weights, that can measure any whole number of kilograms (1,2,3, etc) ...<br />
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<br />
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a) ... up to 15 kg ?<br />
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b) ... up to 40 kg ?<br />
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c) ... up to 80 kg ?</div></div><div class="puzSep"></div><div class="puzSoln"><h2>Our Solution:</h3><div class="puzSolnText">a) Up to 15 kg: <br />
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<br />
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Weights are: 1 kg, 2 kg, 4 kg, 8 kg<br />
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<br />
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Like this:<br />
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<br />
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1 kg = 1 kg<br />
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2 kg = 2 kg<br />
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3 kg = 2 kg + 1 kg<br />
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...<br />
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14 kg = 8 kg + 4kg + 2 kg<br />
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15 kg = 8 kg + 4 kg + 2 kg + 1 kg<br />
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<br />
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b) Up to 40 kg:<br />
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<br />
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Weights are: 1 kg, 3 kg, 9 kg, 27 kg<br />
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<br />
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Like this:<br />
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<br />
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You can put the weights on the other side of the balance, therefore subtracting some of the weight from the other side. Using this system the objects can be weighed thus:<br />
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<br />
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1kg = 1kg<br />
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2kg = 3kg - 1kg<br />
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3kg = 3kg<br />
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...<br />
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39kg = 27kg + 9kg + 3kg<br />
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40kg = 27kg + 9kg + 3kg + 1kg<br />
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<br />
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c) Up to 80 kg:<br />
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<br />
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Weights are: 2 kg, 6 kg, 18 kg, 54 kg<br />
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<br />
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Like this:<br />
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<br />
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Put 2kg on one side, your item on the other. If item is less then 2kg, it is 1 kg. <br />
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If it is more, put 6kg on one side, your item and 2kg on the other. If item and 2kg are less then 6kg, item is 3kg. <br />
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If it is more, put 6kg on one side, your item on the other. If item is less then 6kg, it's 5kg.<br />
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...<br />
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etc, up to 80 kg</div></div><div class="puzSolnFtr">See this puzzle <a href="measuring-kilograms.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="measuring-puzzles-index.html">Measuring Puzzles</a><a href="index.html">Puzzles Index</a></div><!-- #EndEditable --></div>
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