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185 lines
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185 lines
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<title>24 from 8,8,3,3 Puzzle - Solution</title>
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<h1 class="puzTitle">24 from 8,8,3,3 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="24 from 8,8,3,3" style="border-style: none" /></div>
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<p>How can I get the answer 24 by only using the numbers 8, 8, 3 and 3.</p>
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<p>You can use add, subtract, multiply, divide, and parentheses.</p>
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<p>Bonus rules: also allowed are logarithms, factorials and roots</p>
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<p>(Puzzle supplied by "Steve123")</p></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">1) Supplied by "mathsyperson": <br />
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8/(3-(8/3))<br />
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= 8/(1/3)<br />
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= 24<br />
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<br />
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2) Supplied by "puzzler09" (using bonus rules): <br />
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((8 x 3!)/3)+8<br />
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= ((8 × 3 × 2 × 1)/3)+8<br />
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= (48/3)+8<br />
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= (16)+8<br />
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= 24<br />
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<br />
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3) Supplied by "Mark" (using bonus rules): <br />
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(3!/√8)*8<br />
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<br />
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4) Supplied by "Daryl S" (using bonus rules): <br />
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(8-3)!/(8-3) <br />
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(√8 × √8)!<br />
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(√8 + √8)!<br />
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√(8×8×3×3) <br />
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8+(8×(3!/3))<br />
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((√(8+8) × (3/3))!<br />
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√(8+8) × (3+3)<br />
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(log base(3!/3) of 8) × 8<br />
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((log base(3!/3) of (8+8))!<br />
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<br />
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5) Supplied by "Sunil Prajapati" (using bonus rules): <br />
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√(8×8)×√(3×3) which is a variation of √(8×8×3×3) by Daryl S<br />
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<br />
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6) Supplied by "Robert Veith" (using bonus rules): <br />
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(3! - 3) x √(8 × 8)<br />
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(3 + (3(8 - 8))!)!<br />
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(3! - 3 + 8/8)!<br />
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(3! - 3 + (8 - 8)!)!<br />
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(3! x 8)/(8 - 3!)<br />
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(3 + √(8 - 8)!)!<br />
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(3 + √(8/8))!<br />
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3!/(3/8) + 8 = 24<br />
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<br />
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38 - 8 - 3!<br />
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3! × √(8 × 8)<br />
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(8 + 8 - 3! - 3!)!<br />
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(8 - 3! + √8)!<br />
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(√(8 + 8 + 3 - 3))!<br />
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((8 - 3!)(√8))!<br />
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8 × 3! - 8 × 3<br />
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(3! + 3!) × √(√(8 + 8))<br />
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(3 + 3 - √(√(8 + 8)))!<br />
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(3! - 3)! × √(8 + 8)<br />
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√(3! × 3!) × √(8 + 8)<br />
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(8/(8 - (√(3! + 3))!))!<br />
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(8/(8 - √(3! × 3!)))!<br />
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(8/(8 - 3 - 3))!<br />
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(8/(8 - (3! - 3)!))!<br />
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(8/(8 - (√(3 × 3))!))!<br />
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(√3! × 3!) - √(√(8 + 8)))!<br />
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(√((8 - √(3! × 3!)) × 8))!<br />
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(3! - √(8/(8 - 3!)))!<br />
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(√(3! + 3) + 8/8)!<br />
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(√(3! + 3) + (8 - 8)!)!<br />
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(√((8 - (√3! + 3))!) × 8))!<br />
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(√((8 - (√(3 × 3))!) × 8))!<br />
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(√((8 - (3! - 3)!) × 8))!<br />
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3! × √(8 × √8)<br />
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((8 - 3!)(8 - 3!))!<br />
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(√(3 × 8/3 + 8))!<br />
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(3! × 8)/√8 <br />
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(3! × √8 - 8)!<br />
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3! × √(8√8)<br />
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√(8 + 8) × (√(3! + 3))!<br />
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((3 - 3)! × √(8 + 8))!<br />
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8√((3 × 3)!/8!)<br />
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(√(8 × 8)/(3!/3))!<br />
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(3! - 3) × √(8 × 8)<br />
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√(3! + 3) × √(8 × 8)<br />
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8√((3! + 3)!/8!)<br />
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-8 × (log base(3/3!) of 8)<br />
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(-(log base(3/3!) of (8 + 8)))!<br />
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(√(8 + 8) × (log base(3) of 3))!<br />
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(√(3! + 3) + (log base(8) of 8))!<br />
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(√(3 × 3) + (log base(8) of 8))!<br />
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(3 + (log base(8) of 8)) × 3!<br />
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(3! - 3 + (log base(8) of 8))!<br />
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(3! - √(3 + (log base(8) of 8)))!<br />
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(3 + √(log base(8) of 8))!<br />
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(√(8 + 8 × (log base(3) of 3)))!</div></div>
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