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124 lines
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124 lines
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<h1 class="puzTitle">Rhind Papyrus 100 Loaves 5 Men Puzzle - Solution</h1>
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<div class="puzPuzzle"><h2>The Puzzle:</h2>
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<div class="puzThumb"><img src="images/bread.svg" alt="Rhind Papyrus 100 Loaves 5 Men" style="border-style: none" /></div>
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About 2000 years BC there lived Ahmes, a royal secretary and mathematician of the Pharaoh Amenemhat III. One of his papyruses was found in 1853 by an Englishman called Rhind near the temple of Ramses II in Thebes. It has many mathematical puzzles and here is one:<br />
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<br />
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100 loaves of bread must be divided among five workers.<br />
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<br />
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Each worker in line must get more than the previous: the same amount more in each case (an arithmetical progression).<br />
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<br />
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And the first two workers shall get seven times less than the three others.<br />
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<br />
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How many loaves (including fractions of a loaf!) does each worker get?<br />
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<br />
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<br />
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</div>
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<div class="puzSoln"><h2>Our Solution:</h3>
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<div class="puzSolnText">Let us say the middle worker (worker 3) gets "w" loaves.<br />
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And that "d" is the common difference between workers.<br />
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<br />
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So the workers get:<br />
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w-2d<br />
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w-d<br />
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w<br />
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w+d<br />
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w+2d<br />
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<br />
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<br />
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The middle worker gets a perfect average, so 100/5 = 20 loaves<br />
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<br />
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The first two workers get seven times less than the three others:<br />
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7*[(20-2d) + (20-d)] = 20 + (20+d) + (20+2d)<br />
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<br />
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From this: d = 220/24, or 55/6<br />
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<br />
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And this is the solution:<br />
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<br />
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1st worker = 10/6 loaves<br />
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2nd worker = 65/6 loaves<br />
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3rd worker = 120/6 (20) loaves<br />
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4th worker = 175/6 loaves<br />
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5th worker = 230/6 loaves</div></div>
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<div class="puzSolnFtr">See this puzzle <a href="rhind-papyrus-100-loaves-5-men.html">without solution</a><br /></div>
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