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165 lines
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165 lines
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<title>Eight eights Puzzle - Solution</title>
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<h1 class="puzTitle">Eight eights Puzzle - Solution</h1>
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<div class="puzPuzzle"><h2>The Puzzle:</h2>
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<div class="puzText">
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<div class="puzThumb"><img src="images/numbers.svg" alt="Eight eights" style="border-style: none" /></div>
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Use 8 exactly eight times to make 1000<br />
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<br />
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a) Using only + − × /<br />
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b) Also allowing √, exponents ^, factorials !, and decimal points.</div>
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</div>
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<div class="puzSep"></div>
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<div class="puzSoln"><h2>Our Solution:</h3>
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<div class="puzSolnText"><b>A) Using only + − × /</b><br />
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<br />
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<i>By Shivani Dixit:</i><br />
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888 + 88 + 8 + 8 + 8 <br />
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<br />
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<i>by Patrick Saunders:</i><br />
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(8(8(8+8)-(8+8)/8))-8 <br />
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<br />
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<br />
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<i>By Daryl S:</i>:<br />
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(888-8) + 8×(8+8) - 8<br />
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((8×(8+8))-((8+8+8)/8))×8<br />
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((8×(8+8))-((88/8)-8))×8<br />
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(8888-888)/8<br />
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<br />
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<i>By Manoj Kumar Nanduri:</i><br />
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8(8×8+8×8)-8-8-8<br />
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<br />
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<br />
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<br />
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<b>B) Also allowing √, ^, ! and decimal points</b><br />
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<br />
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<i>by Year 10 Set 4 at Lady Manners in Derbyshire:</i><br />
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8888/8.888<br />
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<br />
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<i>By Daryl S:</i>:<br />
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(8+((8+8)/8))^((8+8+8)/8)<br />
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(8+((8+8)/8))^((88/8)-8)<br />
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<br />
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<br />
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<i>By Robert Veith</i>:<br />
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(8888 - 8)/8.88<br />
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(8888 - 88)/8.8<br />
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(888.8 - 8.8)/.88<br />
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88.8/(.8888 - .8)<br />
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8.8/(.8888 - .88)<br />
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888.8/.8888<br />
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(8888 - 88)/8.8<br />
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(8888 - 8)/8.88<br />
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8.8/.88 X 88/.88<br />
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88.8/.888 X 8/.8<br />
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888/.888 X 8/8<br />
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<br />
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<br />
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AND because 10^3=1000 there are 144 solutions made by combining:<br />
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<br />
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Ways to make 10 (using 4 8's):<br />
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(8.8/.88)<br />
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(88/8.8)<br />
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((8 + 8 - 8)/.8)<br />
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(8/(.8 + 8 - 8))<br />
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((88 - 8)/8)<br />
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(√(88/.88))<br />
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((8 + 8)/(.8 + .8))<br />
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(8 + 8/√(8 + 8))<br />
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((8 + 8)/8 + 8)<br />
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(√(8×8) + √(√(8 + 8)))<br />
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(8/8×8/.8)<br />
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(8(8 - 8)!/.8)<br />
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<br />
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Ways to make 3 (using 4 8's):<br />
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((8 + 8 + 8)/8)<br />
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(√(√(8×8) + (8 - 8)!))<br />
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(√(√(8 + 8)) + 8/8)<br />
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(√(8 + 8) - 8/8)<br />
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(88/8 - 8)<br />
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((√(8 + 8)!/√(8×8))<br />
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(√(8 + 8) - (8 - 8)!)<br />
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(√(√(8 + 8)) + (8 - 8)!)<br />
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(√(8/.8 - 8/8))<br />
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(√(√(8×8) + 8/8))<br />
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(√(8/.8 - (8 - 8)!))<br />
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(√(8 + (8(8 - 8))!))</div></div>
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<div class="puzAuthor">Puzzle Author: Shivani Dixit<br /><br /></div>
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<div class="puzSolnFtr">Try more <a href="number-puzzles-index.html">Number Puzzles</a><br>See this puzzle <a href="eight-eights.html">without solution</a><br></div>
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