THE YEAR PUZZLE (program by Heiner Marxen)
Version: $Revision: 1.18 $ $Date: 2006/02/01 17:22:10 $
Target signature = 2008
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 85 of 201 values [42.3%].
     0 = 20*0*8
     1 = 2^0+0*8
     2 = 2+0+0*8
     3 = sqrt(20^0+8)
     4 = sqrt(2*(0+0+8))
     5 = sqrt(200/8)
     6 = -2+0+0+8
     7 = -20^0+8
     8 = 20*0+8
     9 = 20^0+8
    10 = 2+0+0+8
    11 = 20-0!-8
    12 = 20+0-8
    13 = 20+0!-8
    14 = 2*(0-0!+8)
    15 = (2+0!)!+0!+8
    16 = 2*(0+0+8)
    17 = 20-sqrt(0!+8)
    18 = 2*(0!+0+8)
    19 = 20-0!^8
    20 = 20+0*8
    21 = 20+0!^8
    22 = -2+(0!+sqrt(0!+8))!
    23 = 20+sqrt(0!+8)
    24 = (2+0!+0)*8
    25 = 200/8
    26 = 20+sqrt(0!+8)!
    27 = 20-0!+8
    28 = 20+0+8
    29 = 20+0!+8
    30 = 2*(-0!+sqrt(0!+8)!)!!
    31 = ?
    32 = 2*(0!+0!)*8
    33 = .2^(-0!-0!)+8
    34 = ?
    35 = -.2^(-0!)*(0!-8)
    36 = (2+0!)!*sqrt(0!+8)!
    37 = ?
    38 = ?
    39 = ((2+0!)!)!!-0!-8
    40 = sqrt(200*8)
    41 = ((2+0!)!)!!+0!-8
    42 = -(2+0!)!*(0!-8)
    43 = -.2^(-0!)+(sqrt(0!+8)!)!!
    44 = ?
    45 = -2-0!+(sqrt(0!+8)!)!!
    46 = -2+(-0!-0!+8)!!
    47 = ((2+0!)!)!!-0!^8
    48 = (2+0!+0)!*8
    49 = sqrt(sqrt(((2+0!)!+0!)^8))
    50 = 2+(-0!-0!+8)!!
    51 = 2+0!+(sqrt(0!+8)!)!!
    52 = ?
    53 = .2^(-0!)+(sqrt(0!+8)!)!!
    54 = (2+0!)!*(0!+8)
    55 = ((2+0!)!)!!-0!+8
    56 = ((2+0!)!+0!)*8
    57 = ((2+0!)!)!!+0!+8
    58 = ?
    59 = ?
    60 = 20*sqrt(0!+8)
    61 = ?
    62 = -2+sqrt(sqrt(sqrt(sqrt(sqrt(sqrt((0!+0!)^8!!))))))
    63 = (.2^(-0!))!!+(sqrt(0!+8)!)!!
    64 = 2^(-0!-0!+8)
    65 = ?
    66 = 2+sqrt(sqrt(sqrt(sqrt(sqrt(sqrt((0!+0!)^8!!))))))
    67 = ?
    68 = 20+(sqrt(0!+8)!)!!
    69 = -2+sqrt(0!+(-0!+8)!)
    70 = ?
    71 = sqrt(2^0+(-0!+8)!)
    72 = (.2^(-0!))!-(sqrt(0!+8)!)!!
    73 = 2+sqrt(0!+(-0!+8)!)
    74 = ?
    75 = (2+0!)!/.08
    76 = ?
    77 = .20*(0!+8!!)
    78 = ?
    79 = ?
    80 = ((2+0!)!)!/(0!+8)
    81 = sqrt((2+0!+0)^8)
    82 = ?
    83 = ?
    84 = ((2+0!)!+0!)!!*.8
    85 = -20+(-0!+8)!!
    86 = ?
    87 = ?
    88 = sqrt((.2^(-0!))!+0!)*8
    89 = ?
    90 = ((2+0!+0)!)!/8
    91 = ?
    92 = ?
    93 = ?
    94 = -2*(0!-(sqrt(0!+8)!)!!)
    95 = ?
    96 = 2*(-0!-0!+8)!!
    97 = ((2+0!)!+0!)!!-8
    98 = 2*(0!+(sqrt(0!+8)!)!!)
    99 = -(2+0!)!+(-0!+8)!!
   100 = 20/(0!-.8)
   101 = ?
   102 = -2-0!+(-0!+8)!!
   103 = -2+(0-0!+8)!!
   104 = -2^0+(-0!+8)!!
   105 = (-20^0+8)!!
   106 = 2^0+(-0!+8)!!
   107 = 2+(0-0!+8)!!
   108 = 2+0!+(-0!+8)!!
   109 = ?
   110 = .2^(-0!)+(-0!+8)!!
   111 = (2+0!)!+(-0!+8)!!
   112 = ((2+0!)!-0!)!-8
   113 = ((2+0!)!+0!)!!+8
   114 = (.2^(-0!))!-sqrt(0!+8)!
   115 = ?
   116 = ?
   117 = (.2^(-0!))!-sqrt(0!+8)
   118 = -2+(-0!+sqrt(0!+8)!)!
   119 = (.2^(-0!))!-0!^8
   120 = sqrt(200/8)!
   121 = (.2^(-0!))!+0!^8
   122 = 2+(-0!+sqrt(0!+8)!)!
   123 = (.2^(-0!))!+sqrt(0!+8)
   124 = ?
   125 = 20+(-0!+8)!!
   126 = (.2+0!)*(-0!+8)!!
   127 = (.2^(-0!))!-0!+8
   128 = 2^(0-0!+8)
   129 = (.2^(-0!))!+0!+8
   130 = ?
   131 = ?
   132 = ?
   133 = ?
   134 = ?
   135 = (.2^(-0!))!!*(0!+8)
   136 = ?
   137 = ?
   138 = ?
   139 = ?
   140 = -20*(0!-8)
   141 = ?
   142 = 2*sqrt(0!+(-0!+8)!)
   143 = ?
   144 = ((2+0!)!)!!*sqrt(0!+8)
   145 = ?
   146 = ?
   147 = ?
   148 = ?
   149 = ?
   150 = (.2^(-0!))!/0.8
   151 = ?
   152 = (20-0!)*8
   153 = ((2+0!)!)!!+(-0!+8)!!
   154 = ?
   155 = ?
   156 = ?
   157 = ?
   158 = ?
   159 = ?
   160 = 20*(0+8)
   161 = ?
   162 = ?
   163 = ?
   164 = ?
   165 = ?
   166 = ?
   167 = ?
   168 = (20+0!)*8
   169 = ?
   170 = ?
   171 = ?
   172 = ?
   173 = ?
   174 = ?
   175 = ?
   176 = ?
   177 = ?
   178 = ?
   179 = ?
   180 = 20*(0!+8)
   181 = ?
   182 = ?
   183 = ?
   184 = -200+8!!
   185 = ?
   186 = ?
   187 = ?
   188 = ?
   189 = .20*(0!+8)!!
   190 = ?
   191 = ?
   192 = 200-8
   193 = ?
   194 = ?
   195 = ?
   196 = sqrt(sqrt(((.2^(-0!))!!-0!)^8))
   197 = ?
   198 = ?
   199 = sqrt(-((2+0!)!)!+0!+8!)
   200 = sqrt(sqrt(sqrt(200^8)))