THE YEAR PUZZLE (program by Heiner Marxen)
Version: $Revision: 1.18 $ $Date: 2006/02/01 17:22:10 $
Target signature = 2004
Without permutation of signature digits.
Intermediate (de)nominator range = -500000 .. 500000
Result range = 0 .. 200
With standard binary operators: + - * /
With standard  unary operators: - sqrt
With parentheses.
With concatenation.
With exponentiation (^).
With factorial (!).
With even/odd factorial (!!).
With decimal point.
Could not solve 68 of 201 values [33.8%].
     0 = 20*0*4
     1 = 2^0+0*4
     2 = 2+0+0*4
     3 = -20^0+4
     4 = 20*0+4
     5 = 20/(0+4)
     6 = 2+0+0+4
     7 = 2+0!+0+4
     8 = 2*(0+0+4)
     9 = (2+0!)!-0!+4
    10 = 20/(0+sqrt(4))
    11 = (2+0!)!+0!+4
    12 = (2+0!+0)*4
    13 = 2+sqrt(0!+(0!+4)!)
    14 = sqrt(200-4)
    15 = 20-0!-4
    16 = 20+0-4
    17 = 20+0!-4
    18 = 20+0-sqrt(4)
    19 = 20-0!^4
    20 = 20+0*4
    21 = 20+0!^4
    22 = 20+0+sqrt(4)
    23 = 20-0!+4
    24 = 20+0+4
    25 = 20+0!+4
    26 = 2+0+0+4!
    27 = 2+0!+0+4!
    28 = 2+0!+0!+4!
    29 = (2+0!)!-0!+4!
    30 = (2+0!)!+0+4!
    31 = (2+0!)!+0!+4!
    32 = 2^(0!+0+4)
    33 = ((2+0!)!)!!-(0!+4)!!
    34 = ?
    35 = 20+(0!+4)!!
    36 = (2+0!+0)!^sqrt(4)
    37 = ?
    38 = (20-0!)*sqrt(4)
    39 = ((2+0!)!-0!)!!+4!
    40 = 20*(0+sqrt(4))
    41 = ((2+0!)!)!!+0!-4!!
    42 = (20+0!)*sqrt(4)
    43 = 20-0!+4!
    44 = 20+0+4!
    45 = 20+0!+4!
    46 = 2*(0-0!+4!)
    47 = ((2+0!)!)!!-0!^4
    48 = 2*(0+0+4!)
    49 = ((2+0!)!+0!)^sqrt(4)
    50 = 200/4
    51 = ((2+0!)!)!!-0!+4
    52 = 2*(0!+0!+4!)
    53 = ((2+0!)!)!!+0!+4
    54 = (2+0!)!*(0!+4!!)
    55 = ((2+0!)!)!!-0!+4!!
    56 = ((2+0!)!+0!)*4!!
    57 = ((2+0!)!)!!+0!+4!!
    58 = ?
    59 = ?
    60 = -20*(0!-4)
    61 = ?
    62 = -2+sqrt(sqrt((0!+0!)^4!))
    63 = ((2+0!)!)!!+(0!+4)!!
    64 = 2^(0!+0!+4)
    65 = ?
    66 = 2+sqrt(sqrt((0!+0!)^4!))
    67 = ?
    68 = 20+((-0!+4)!)!!
    69 = (2+0!)*(-0!+4!)
    70 = ?
    71 = ((2+0!)!)!!-0!+4!
    72 = (2+0!+0)*4!
    73 = ((2+0!)!)!!+0!+4!
    74 = ?
    75 = (2+0!)*(0!+4!)
    76 = (20-0!)*4
    77 = .20*(0!+(4!!)!!)
    78 = ?
    79 = ?
    80 = 20*(0+4)
    81 = (2+0!+0)^4
    82 = ?
    83 = ?
    84 = (20+0!)*4
    85 = -20+(-0!+4!!)!!
    86 = ?
    87 = ?
    88 = sqrt((.2^(-0!))!+0!)*4!!
    89 = ?
    90 = (2+0!)!*(0!+4)!!
    91 = ?
    92 = ?
    93 = ?
    94 = -2*(0!-((-0!+4)!)!!)
    95 = (.2^(-0!))!-0!-4!
    96 = 2*(0!+0!)*4!
    97 = ((2+0!)!+0!)!!-4!!
    98 = 2*(0!+((-0!+4)!)!!)
    99 = -(2+0!)!+(-0!+4!!)!!
   100 = 200/sqrt(4)
   101 = ((2+0!)!+0!)!!-4
   102 = -2-0!+(-0!+4!!)!!
   103 = -2+(-0!+0+4!!)!!
   104 = -2^0+(-0!+4!!)!!
   105 = (2+0!+0+4)!!
   106 = 2^0+(-0!+4!!)!!
   107 = 2+(-0!+0+4!!)!!
   108 = 2+0!+(-0!+4!!)!!
   109 = ((2+0!)!+0!)!!+4
   110 = .2^(-0!)+(-0!+4!!)!!
   111 = (2+0!)!+(-0!+4!!)!!
   112 = ((2+0!)!-0!)!-4!!
   113 = ((2+0!)!+0!)!!+4!!
   114 = -(2+0!)!+(0!+4)!
   115 = (.2^(-0!))!-0!-4
   116 = ((2+0!)!-0!)!-4
   117 = -2-0!+(0!+4)!
   118 = -2+(0!+0+4)!
   119 = -2^0+(0!+4)!
   120 = (2^0+0+4)!
   121 = 2^0+(0!+4)!
   122 = 2+(0!+0+4)!
   123 = 2+0!+(0!+4)!
   124 = ((2+0!)!-0!)!+4
   125 = sqrt(sqrt(sqrt(((2+0!)!-0!)^4!)))
   126 = (2+0!)!+(0!+4)!
   127 = (.2^(-0!))!-0!+4!!
   128 = 2^(0!+(-0!+4)!)
   129 = ((2+0!)!+0!)!!+4!
   130 = ?
   131 = ?
   132 = ?
   133 = ?
   134 = ?
   135 = (.2^(-0!))!!+(0!+4)!
   136 = ?
   137 = ?
   138 = -(2+0!)!*(0!-4!)
   139 = ?
   140 = 20+(0!+4)!
   141 = ?
   142 = 2*sqrt(0!+(-0!+4!!)!)
   143 = (.2^(-0!))!-0!+4!
   144 = (2+0!+0)!*4!
   145 = (.2^(-0!))!+0!+4!
   146 = ?
   147 = ?
   148 = ?
   149 = ?
   150 = (2+0!)!*(0!+4!)
   151 = ?
   152 = (20-0!)*4!!
   153 = ((2+0!)!)!!+(-0!+4!!)!!
   154 = ?
   155 = ?
   156 = ?
   157 = ?
   158 = ?
   159 = ?
   160 = 20*(0+4!!)
   161 = ?
   162 = ?
   163 = ?
   164 = ?
   165 = ?
   166 = ?
   167 = ?
   168 = ((2+0!)!+0!)*4!
   169 = ?
   170 = ?
   171 = ?
   172 = ?
   173 = ?
   174 = ?
   175 = ?
   176 = 200-4!
   177 = ?
   178 = ?
   179 = ?
   180 = ((2+0!+0)!)!/4
   181 = ?
   182 = ?
   183 = ?
   184 = -200+(4!!)!!
   185 = ?
   186 = ?
   187 = ?
   188 = (((2+0!)!)!!-0!)*4
   189 = .20*(0!+4!!)!!
   190 = ?
   191 = ?
   192 = 200-4!!
   193 = ?
   194 = ?
   195 = ?
   196 = 200-4
   197 = ?
   198 = 200-sqrt(4)
   199 = sqrt(-((2+0!)!)!+0!+(4!!)!)
   200 = sqrt(200^sqrt(4))