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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>
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<h1 class="puzTitle">Four Fours Puzzle - Solution</h1>
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<div class="puzPuzzle">
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<h2>The Puzzle:</h2>
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<div class="puzText">
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<div class="puzThumb"><img src="images/numbers.svg" alt="Four Fours" style="border-style: none" height="86" width="88" ></div>
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<p>A popular mathematical pastime:</p>
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<p>Use exactly four 4's to form every integer from 0 to 50, using only the operators +, −, ×, /, () (brackets), . (decimal point), √ (square root) and ! (factorial).</p>
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<p>Example: 0 = 44 − 44</p></div>
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</div>
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<div class="puzSep"></div>
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<div class="puzSoln">
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<h2>Our Solution:</h3>
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<div class="puzSolnText">Here is our list of solutions:<br>
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<br>
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0 = 44 − 44<br>
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1 = 44 / 44 or (4 + 4)/(4 + 4) or (4/4) / (4/4) or ((4! − 4) / 4) − 4<br>
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2 = 4/4 + 4/4<br>
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3 = (4 + 4 + 4) / 4<br>
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4 = 4 × (4 − 4) + 4<br>
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5 = (4 × 4 + 4) / 4<br>
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6 = 4 × .4 + 4.4<br>
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7 = 44 / 4 − 4<br>
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8 = 4 + 4.4 − .4<br>
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9 = 4/4 + 4 + 4<br>
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10 = 44 / 4.4<br>
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11 = 4/.4 + 4/4<br>
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12 = (44 + 4) / 4<br>
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13 = 4! − 44/4<br>
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14 = 4 × (4 − .4) − .4<br>
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15 = 44 / 4 + 4<br>
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16 = .4 × (44 − 4)<br>
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17 = 4/4 + 4 × 4<br>
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18 = 44 × .4 + .4<br>
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19 = 4! − 4 − 4/4<br>
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20 = 4 × (4/4 + 4)<br>
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21 = (4.4 + 4)/.4<br>
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22 = 44 × √4 / 4<br>
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23 = (4 × 4! − 4)/ 4<br>
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24 = 4 × 4 + 4 + 4<br>
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25 = (4 × 4! + 4) / 4<br>
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26 = 4/.4 + 4×4<br>
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27 = 4 − 4/4 + 4!<br>
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28 = 44 − 4 × 4<br>
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29 = 4/.4/.4 + 4<br>
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30 = (4 + 4 + 4) / .4<br>
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31 = (4! + 4) / 4 + 4!<br>
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32 = 4 × 4 + 4 × 4<br>
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33 = (4 − .4)/.4 + 4!<br>
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34 = 44 − 4/.4<br>
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35 = 44 / 4 + 4!<br>
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36 = 44 − 4 − 4<br>
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37 = (√4 + 4!)/√4 + 4!<br>
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38 = 44 − 4!/4<br>
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39 = (4 × 4 − .4)/.4<br>
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40 = 44 − √(4 × 4)<br>
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41 = (√4 + 4!)/.4 − 4!<br>
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42 = √4 + 44 − 4<br>
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43 = 44 − 4/4<br>
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44 = 44.4 − .4<br>
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45 = 4/4 + 44<br>
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46 = 44 − √4 + 4<br>
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47 = 4! + 4! − 4/4<br>
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48 = 4 × (4 + 4 + 4)<br>
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49 = (4! − 4.4) / .4<br>
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50 = 4! / 4 + 44<br>
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<br>
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<br>
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BONUS! 51 to 100, but we have gaps. Can you fill them in?<br>
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<br>
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51 = (4! − 4 + .4) / .4<br>
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52 = 44 + 4 + 4<br>
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53<br>
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54 = 4! + 4! + (4! / 4)<br>
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55<br>
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56 = 44 + 4! / √4<br>
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57<br>
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58 = 4! + 4! + 4/.4<br>
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59 = 4!/.4 − 4/4<br>
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60 = 44 + 4 × 4<br>
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61 = 4!/.4 + 4/4<br>
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62 = (4 + 4) ^ √4 − √4<br>
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63 = (4! + √4) / .4 − √4<br>
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64 = 4 × 4 × √4 × √4<br>
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65 = (4^4 +4) / 4<br>
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66 = (4 + 4) ^ (√4) + √4<br>
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67 = (4! + √4) / .4 + √4<br>
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68 = (4 + 4) ^ √4 + 4<br>
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69 = (4! + 4 − .4) / .4<br>
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70 = 44 + 4! + √4<br>
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71 = (4 + 4! + .4) / .4<br>
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72 = (4! / 4) ^ √4 × √4<br>
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73<br>
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74 = 4! + 4! + 4! + √4<br>
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75 = (4! + √4 + 4) / .4<br>
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76 = 4! × 4 − 4! + 4<br>
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77<br>
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78<br>
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79<br>
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80 = 4! × 4 − 4×4<br>
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81<br>
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82 = 4! / .4 + 4! − √4<br>
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83<br>
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84 = 4! × 4 − 4! / √4<br>
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85<br>
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86 = 4! × 4 − 4/.4<br>
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87<br>
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88 = 4! × 4 − 4 − 4<br>
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89 = 4! + (4! + √4) / .4<br>
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90 = 4! × 4 − 4! / 4<br>
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91 = 4 × 4! − √4 / .4<br>
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92 = 4! × (√4 + √4) − 4<br>
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93<br>
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94 = 4! × 4 − 4/√4<br>
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95 = 4! × 4 − 4/4<br>
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96 = 4! × 4 + 4 − 4<br>
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97 = 4! × 4 + 4/4<br>
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98 = 4! × 4 + 4/√4<br>
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99<br>
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100 = 4! × 4 + √4 + √4<br>
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<br>
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(Note: people have managed to do this for 1000s of numbers)</div></div>
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<div class="puzSolnFtr">Try more <a href="number-puzzles-index.html">Number Puzzles</a><br>
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See this puzzle <a href="four-fours.html">without solution</a><br>
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