Four Fours Puzzle


  • Posted by  downloadmela 
    10 Feb, 2012

    A popular mathematical pastime:

    Use exactly four 4's to form every integer from 0 to 50, using only the operators +, -, x, /, () (brackets) x2 (square), and ! (factorial).



    Solution
    0 = 44-44
    1 = 44/44 or (4+4)/(4+4) or (4/4) / (4/4) or [(4! - 4)/ 4] - 4
    2 = 4/4+4/4 or (42-4-4)/4
    3 = (4+4+4)/4
    4 = 4*(4-4)+4
    5 = (4*4+4)/4
    6 = 4*.4+4.4
    7 = 44/4-4
    8 = 4+4.4-.4
    9 = 4/4+4+4
    10 = 44/4.4
    11 = 4/.4+4/4
    12 = (44+4)/4
    13 = 4!-44/4
    14 = 4*(4-.4)-.4
    15 = 44/4+4
    16 = .4*(44-4)
    17 = 4/4+4*4
    18 = 44*.4+.4
    19 = 4!-4-4/4
    20 = 4*(4/4+4)
    21 = (4.4+4)/.4
    22 = 44*sqrt(4)/4
    23 = (4*4!-4)/4
    24 = 4*4+4+4
    25 = (4*4!+4)/4
    26 = 4/.4+4*4
    27 = 4-4/4+4!
    28 = 44-4*4
    29 = 4/.4/.4+4
    30 = (4+4+4)/.4
    31 = (4!+4)/4+4!
    32 = 4*4+4*4
    33 = (4-.4)/.4+4!
    34 = 44-4/.4
    35 = 44/4+4!
    36 = 44-4-4
    37 = (sqrt(4)+4!)/sqrt(4)+4!
    38 = 44-4!/4
    39 = (4*4-.4)/.4
    40 = 44-sqrt(4*4)
    41 = (sqrt(4)+4!)/.4-4!
    42 = sqrt(4)+44-4
    43 = 44-4/4
    44 = 44.4-.4
    45 = 4/4+44
    46 = 44-sqrt(4)+4
    47 = 4!+4!-4/4
    48 = 4*(4+4+4)
    49 = (4!-4.4)/.4
    50 = 4!/4+44




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