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123 lines
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<h1 class="puzTitle">Number Sequences 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="Number Sequences" style="border-style: none" /></div>
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There are infinitely many formulas that will fit any finite series. <br />
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<br />
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Try to guess the next number in each sequence using the simplest mathematical operations or ideas (you may get a different answer than my solution though):<br />
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<br />
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· 8723, 3872, 2387, ?<br />
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· 1, 4, 9, 18, 35, ?<br />
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· 23, 45, 89, 177, ?<br />
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· 7, 5, 8, 4, 9, 3, ?<br />
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· 3, 8, 15, 24, 35, ?<br />
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· 2, 4, 5, 10, 12, 24, 27, ?<br />
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· 1, 3, 4, 7, 11, 18, ?<br />
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· 99, 92, 86, 81, 77, ?<br />
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· 0, 4, 2, 6, 4, 8, ?<br />
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· 1, 2, 6, 24, 120, ?<br />
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· 5, 7, 12, 19, 31, 50, ?<br />
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· 31, 94, 47, 142, 71, 214, 107, 322, 161, ?<br />
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· 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, ?<br />
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· 4, 7, 15, 29, 59, 117, ?<br />
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· 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, ?</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">You may have come up with other good and well-reasioned answers, but here are the ones I have:<br />
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<br />
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· 8723, 3872, 2387, => 7238 (moving of numerals)<br />
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· 1, 4, 9, 18, 35, => 68 (×2+2, ×2+1, ×2+0, ×2-1, ×2-2, ...)<br />
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· 23, 45, 89, 177, => 353 (×2-1, ...)<br />
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· 7, 5, 8, 4, 9, 3, => 10, 2 (two series - every second number: 7, 8, 9, 10 and 5, 4, 3, 2)<br />
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· 3, 8, 15, 24, 35, => 48 (+5, +7, +9, +11, +13, ...)<br />
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· 2, 4, 5, 10, 12, 24, 27, => 54, 58 (×2, +1, ×2, +2, ×2, +3, ×2, +4, ...)<br />
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· 1, 3, 4, 7, 11, 18, => 29 (a+b=c, b+c=d, c+d=e, ...)<br />
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· 99, 92, 86, 81, 77, => 74 (-7, -6, -5, -4, -3, ...)<br />
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· 0, 4, 2, 6, 4, 8, => 6 (+4, -2, +4, -2, +4, -2, ...)<br />
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· 1, 2, 6, 24, 120, =>720 (×2, ×3, ×4, ×5, ×6, ...)<br />
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· 5, 7, 12, 19, 31, 50, => 81 (a+b=c, b+c=d, c+d=e, ...)<br />
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· 31, 94, 47, 142, 71, 214, 107, 322, 161 => 484 (×3+1, /2, ×3+1, /2, ...)<br />
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· 126, 63, 190, 95, 286, 143, 430, 215, 646, 323, 970, => 485, 1456 (/2, ×3+1, /2, ×3+1, ...)<br />
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· 4, 7, 15, 29, 59, 117, => 235 (×2-1, ×2+1, ×2-1, ...)<br />
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· 4, 4, 341, 6, 4, 4, 6, 6, 4, 4, 6, 10, 4, 4, 14, 6, 4, 4, 6, 6, 4, 4, 6, 22, 4, 4, 9, 6, => 4, 4</div></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="number-sequences.html">without solution</a><br></div>
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