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3 <!-- Mirrored from users.eniinternet.com/bradleym/Magic.html by HTTrack Website Copier/3.x [XR&CO'2014], Sun, 06 Nov 2022 06:49:09 GMT -->
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4 <head>
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5 <title></title>
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6 </head>
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7 <body text="#000000" link="#0000ff" vlink="#551a8b" alink="#ff0000" bgcolor="#c0c0c0">
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8
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9 <p><hr>
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10
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11 <br wp="br1"><br wp="br2"><a name="The Magic Of Go">
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12 <p><strong>The Magic Of Go</strong>
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13
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14 <p><strong>© 2002 Milton N. Bradley</a></strong>
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15
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16 <p>Although the characteristic which places Go on a unique plane far above competitors like chess
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17 is its almost unbelievably profound strategy, it is the clever, incisive tactics of Go that are the
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18 most obvious and accessible feature which provides much of its appeal.
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19
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20 <p>As in chess, perhaps the most startling and frequently unexpected of Go's extensive catalog of
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21 clever tactical ploys is the sacrifice, so this will be the focus of many of the few selected
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22 examples presented here.
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23
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24 <p>Unlike chess, in which many of the best problems can be shown to be impossible to achieve in a
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25 real game, EVERY GO PROBLEM IS COMPLETELY REALISTIC and the vast majority of the
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26 best ones have actually occurred in master games! <a href="#Problem 1">
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27
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28 <p>Problem 1</a> - Elementary <a href="#Problem 2">
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29
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30 <p>Problem 2</a> - Elementary <a href="#Problem 3">
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31
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32 <p>Problem 3</a> - Easy <a href="#Problem 4">
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33
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34 <p>Problem 4</a> - Easy <a href="#Problem 5">
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35
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36 <p>Problem 5</a> - Intermediate <a href="#Problem 6">
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37
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38 <p>Problem 6</a> - Intermediate <a href="#Problem 7">
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39
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40 <p>Problem 7</a> - Somewhat Difficult <a href="#Problem 8">
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41
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42 <p>Problem 8</a> - Somewhat Difficult <a href="#Problem 9">
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43
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44 <p>Problem 9</a> - Moderately Difficult <a href="#Problem 10">
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45
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46 <p>Problem 10</a> - Moderately Difficult
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47
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48 <p>The examples presented here provide only a tiny insight into the beautiful and challenging world
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49 of Go problems. For a vastly greater and more advanced selection, please refer to the section
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50 entitled "Problems" in the wonderful <a href="http://nngs.cosmic.org/hmkw/golinks.html"></font><font color="#0033ff"><strong>The Web Go Page Index</strong></font><font color="#0000ff"></a></font>
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51
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52 <p>After you've had your fill of those brain twisters (at least for the moment) please don't forget to
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53 return here for the remainder of my presentation!<a href="Legend.html">
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54
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55 <p><font color="#0033ff"><strong>Continue</strong></font></a>
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56
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57 <p>Click Here To Return To<a href="index.html"><font color="#0033ff"><strong> Milt's Go Page</strong></font></a>
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58
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59 <p><hr>
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60 <br wp="br1"><br wp="br2"><a name="Problem 1">
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61 <p>Problem 1</a> - Black To Play And Live
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62
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63 <p><font color="#0000ff"><img src="img.gif" width="122" height="122" align="bottom" ></font>
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64
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65 <p>Click here to see the <a href="#Problem 1 Solution">Solution And Explanation</a>
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66
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67 <p><hr>
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68 <a name="Problem 2">
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69 <p>Problem 2</a> - Black To Play And Kill
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70
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71 <p><img src="img1.gif" width="102" height="262" align="left" >
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72 <br wp="br1"><br wp="br2">
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73 <br wp="br1"><br wp="br2">
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74 <br wp="br1"><br wp="br2">
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75 <br wp="br1"><br wp="br2">
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76 <br wp="br1"><br wp="br2">
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77 <br wp="br1"><br wp="br2">
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78 <br wp="br1"><br wp="br2">
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79 <br wp="br1"><br wp="br2">
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80
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81 <p>Click here to see the <a href="#Problem 2 Solution">Solution And Explanation</a>
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82
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83 <p><hr><br wp="br1"><br wp="br2"><a name="Problem 3">
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84 <p>Problem 3</a> - White to play and kill the Black upper left corner.
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85
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86 <p><img src="img2.gif" width="162" height="202" align="left" ></font>
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87 <br wp="br1"><br wp="br2">
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88 <br wp="br1"><br wp="br2">
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89 <br wp="br1"><br wp="br2">
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90 <br wp="br1"><br wp="br2">
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91 <br wp="br1"><br wp="br2">
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92 <br wp="br1"><br wp="br2">
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93
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94 <p>Click here to see the<a href="#Problem 3 Solution"> Solution And Explanation</a>
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95
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96 <p><hr>
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97
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98 <br wp="br1"><br wp="br2"><a name="Problem 4">
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99 <p>Problem 4</a> - White to play and live in the upper left corner.
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100
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101 <p><img src="img3.gif" width="202" height="222" align="left" ></font>
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102 <br wp="br1"><br wp="br2">
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103 <br wp="br1"><br wp="br2">
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104 <br wp="br1"><br wp="br2">
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105 <br wp="br1"><br wp="br2">
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106 <br wp="br1"><br wp="br2">
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107 <br wp="br1"><br wp="br2">
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108 <p>Click here to see the <a href="#Problem 4 Solution">Solution and Explanation</a>
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109
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110 <p><hr>
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111
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112 <br wp="br1"><br wp="br2"><a name="Problem 5">
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113 <p>Problem 5</a> - Black to play and live despite the fact that the marked White stone has just been
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114 played on his key point!
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115 <p><img src="img4.gif" width="193" height="97" align="left" >
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116
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117 <br wp="br1"><br wp="br2">
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118 <br wp="br1"><br wp="br2">
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119 <br wp="br1"><br wp="br2">
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120 <p>Click here to see the <a href="#Problem 5 Solution">Solution And Explanation</a>
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121
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122 <p><hr>
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123 </font>
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124 <br wp="br1"><br wp="br2"><a name="Problem 6">
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125 <p>Problem 6</a> - Black to Play For Ko
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126 <p><img src="img5.gif" width="122" height="142" align="left" >
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127
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128 <br wp="br1"><br wp="br2">
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129 <br wp="br1"><br wp="br2">
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130 <br wp="br1"><br wp="br2">
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131 <br wp="br1"><br wp="br2">
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132 <br wp="br1"><br wp="br2">
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133 <p>Click here to see the <a href="#Problem 6 Solution">Solution And Explanation</a>
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134
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135 <p><hr>
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136 </font>
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137 <br wp="br1"><br wp="br2"><a name="Problem 7">
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138 <p>Problem 7</a> - Black To Play And Live (Despite the fact that the marked White stone has just been
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139 played.)
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140
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141 <p><img src="img6.gif" width="142" height="182" align="left" >
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142
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143 <br wp="br1"><br wp="br2">
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144 <br wp="br1"><br wp="br2">
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145 <br wp="br1"><br wp="br2">
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146 <br wp="br1"><br wp="br2">
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147 <br wp="br1"><br wp="br2">
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148 <br wp="br1"><br wp="br2">
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149 <p>Click here to see the <a href="#Problem 7 Solution">Solution And Explanation</a>
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150
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151 <p><hr>
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152
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153 <br wp="br1"><br wp="br2"><a name="Problem 8">
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154 <p>Problem 8</a> - Black To Play And Kill
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155
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156 <p><img src="img7.gif" width="122" height="162" align="left" >
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157
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158 <br wp="br1"><br wp="br2">
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159 <p>Here, The white stones have excellent shape and a solid root in the corner,
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160 so killing them can only be achieved via the most precise play.
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161
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162 <br wp="br1"><br wp="br2">
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163 <br wp="br1"><br wp="br2">
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164 <br wp="br1"><br wp="br2">
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165 <p>Click here to see the <a href="#Problem 8 Solution">Solution And Explanation</a>
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166
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167 <p><hr>
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168 </font>
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169 <br wp="br1"><br wp="br2"><a name="Problem 9">
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170 <p>Problem 9</a> - Black To Play And Live
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171
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172 <p><img src="img8.gif" width="162" height="122" align="left" >
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173
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174 <br wp="br1"><br wp="br2">
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175 <br wp="br1"><br wp="br2">
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176 <br wp="br1"><br wp="br2">
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177 <br wp="br1"><br wp="br2">
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178 <p>Click here to see the <a href="#Problem 9 Solution">Solution And Explanation</a>
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179
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180 <p><hr>
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181 </font>
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182 <br wp="br1"><br wp="br2"><a name="Problem 10">
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183 <p>Problem 10</a> - Black to Play And Kill
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184
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185 <p><img src="img9.gif" width="162" height="142" align="left" >
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186
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187 <br wp="br1"><br wp="br2">
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188 <br wp="br1"><br wp="br2">
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189 <br wp="br1"><br wp="br2">
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190 <br wp="br1"><br wp="br2">
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191 <br wp="br1"><br wp="br2">
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192 <p>Click here to see the <a href="#Problem 10 Solution">Solution And Explanation</a><hr>
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193
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194 <br wp="br1"><br wp="br2">
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195 <p><hr>
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196 <a name="Problem 1 Solution">
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197 <p>Problem 1 Solution</a>
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198
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199 <p><img src="img10.gif" width="122" height="122" align="left" >The "rule of thumb" which applies here is "in a symmetrical position, play
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200 at the middle", and with B1 the life of the Black group is assured!
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201
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202 <p>If W2 attempts to narrow Black's eyespace B3 blocks while forming one
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203 eye. Then W4 and B5 repeat the procedure on the other side, giving Black
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204 the 2 separate and distinct eyes needed for life and safety.
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205
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206 <p>By symmetry, W2 and 4 may be played in either order.
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207
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208 <p>Of course, in a game between experienced players, none of this will occur (except as Ko threats
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209 and responses) until the late endgame, since both sides can clearly see that after B1 it is
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210 impossible for White to kill directly.
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211
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212 <p>Please note that whether or not the point "a" is filled (by either side) makes absolutely no
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213 difference to the life or death of these stones! Finally, after B5 White can only defend one or the
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214 other of W2 and 4, so Black is almost certain to be able to capture one of them. <a href="#Problem 2">
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215
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216 <p>Next Problem</a>
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217
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218 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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219
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220 <p><hr>
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221
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222 <br wp="br1"><br wp="br2"><a name="Problem 2 Solution">
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223 <p>Problem 2 Solution</a>
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224
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225 <p><img src="img11.gif" width="102" height="262" align="left" >B1 is the key initial play, on White's eye-making point (if White plays here
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226 instead, he has 3 eyes and is alive!).
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227
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228 <p>Since the position is symmetrical, it makes no difference if W2 is played as
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229 shown or at 5.
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230
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231 <p>Because W2 threatens to continue at 3, not only making one eye but with atari
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232 on the 2 Blacks as well, the additional sacrifice of B3 to prevent this is
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233 necessary.
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234
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235 <p>W4 is not only atari on the 3 Blacks, but also threatens to continue at 5 to form
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236 an eye as well, so B5 to prevent this is essential.
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237
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238 <p>(Note that if W4 is played at 5 instead, B5 at 4 also kills! Please work this
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239 variation out for yourself.)
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240
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241 <p>Finally, W6 could be played to capture the 3 trapped Blacks but this would not
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242 save him because 3 stones in an "L" is a "dead shape", so B7 would be played
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243 back "beneath the stones" at 1 to reduce White to one eye. Therefore the White formation here is
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244 simply "dead as it stands"...... except that there is still a spark of life remaining! Do you see why?
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245
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246 <p>The only chance for life is if White captures the 3 Blacks as a Ko Threat which Black cannot
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247 afford to answer here. Then, White will be the one who can play "beneath the stones" at the point
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248 of 1 to form his 2 eyes after all!
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249
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250 <p>From this analysis, the alert reader may realize that in an actual game between two competent
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251 players in this situation no further moves would be made directly after B1, because White would
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252 "read" out the diagramed sequence mentally and recognize that it failed. So, in practice, ALL of
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253 the diagramed moves would be made ONLY as Ko Threats and responses thereto! (If and when
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254 such a remote Ko came into existence.) <a href="#Problem 3">
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255
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256 <p>Next Problem</a><a href="#Problem 1">
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257
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258 <p>Prior Problem</a>
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259
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260 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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261
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262 <p><hr>
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263
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264 <br wp="br1"><br wp="br2"><a name="Problem 3 Solution">
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265 <p>Problem 3 Solution</a>
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266
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267 <p><img src="img12.gif" width="182" height="202" align="left" >
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268
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269 <br wp="br1"><br wp="br2">
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270
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271 <p>The Black corner group already has one secure eye at "a", but in
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272 order for it to secure the second real eye needed to ensure its
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273 absolute safety (here, at "b"), Black would have to play on the
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274 point now occupied by the marked White stone.
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275
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276 <p>By playing the marked sacrifice stone on this key point himself,
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277 White has converted the point "b" into a FALSE EYE, and
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278 because the Black group cannot escape it is now DEAD AS IT
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279 STANDS. Because these Black stones still have liberties they will
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280 remain on the board until both sides have passed and the game is
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281 over, but then White will simply remove all of them as his
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282 prisoners without further play! <a href="#Problem 2">
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283
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284 <br wp="br1"><br wp="br2">
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285
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286 <p>Prior</a><a href="#Problem 4">
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287
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288 <p>Next</a>
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289
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290 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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291
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292 <p><hr>
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293
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294 <br wp="br1"><br wp="br2"><a name="Problem 4 Solution">
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295 <p>Problem 4 Solution</a>
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296
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297 <p><img src="img13.gif" width="202" height="202" align="top" ><img src="img14.gif" width="202" height="202" align="top" >
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298
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299
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300 <p>W1 is the key sacrifice, giving atari to 3 Black stones.
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301
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302 <p>At this point a competent Black would abandon these stones, because further resistance is futile!
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303
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304
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305 <p>If Black foolishly continues with B2 as shown to capture W1 (and remove it from the board), W3
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306 is again atari on the same 3 Blacks.
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307
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308 <p>If B4 then mistakenly connects, after the inescapable atari of W5 he has lost 6 stones instead of
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309 only 3, but since he has captured W1 his true net loss is "only" 5 stones. With either scenario
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310 White is assured of his necessary 2 eyes, and life in the corner.
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311
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312 <p>This position arose in an actual game between two professional Go masters, played on the
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313 Internet Go Server (IGS) in Feb 1997, but with Black to move instead of White! So, of course,
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314 the opportunity for White to play this sacrificial sequence never occurred because Black foresaw
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315 it and wisely played on the point to the right of W5 to prevent it!
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316
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317 <p>This sort of prophylactic play is quite common at the higher levels, and as a consequence most
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318 (but far from all) of the spectacular tactical ploys in Go occur only in the minds of the players,
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319 and not on the board! <a href="#Problem 3">
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320
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321 <p>Prior</a><a href="#Problem 5">
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322
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323 <p>Next</a>
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324
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325 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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326
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327 <p><hr>
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328 <br wp="br1"><br wp="br2"><a name="Problem 5 Solution">
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329 <p>Problem 5 Solution</a>
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330
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331 <p><img src="img15.gif" width="193" height="97" align="bottom" > <img src="img16.gif" width="193" height="97" align="bottom" > <img src="img17.gif" width="193" height="97" align="bottom" >
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332
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333 <p>B1 makes one eye, and then W2 gives atari to one Black.
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334
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335 <p>B3 captures 2 White stones, and then W4 plays back on the point just vacated by W2 ("beneath
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336 the stones") to again atari the lone Black stone.
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337
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338 <p>Next, if B5 is mistakenly played at the point of 6 to capture W4, the atari of W5 kills Black
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339 because the eye at 4 is false!
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340
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341 <p>So the only feasible response is the connection of B5 as shown, allowing W6 to capture 4
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342 Blacks!
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343
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344 <p>But now it is Black who gets to make the play "beneath the stones" with B7, giving an
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345 inescapable atari to W4, 6 and thereby assuring Black's second eye with their capture!
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346
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347 <p>The secret to success in such situations, of course, is not only being able to visualize the entire
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348 sequence beforehand, but also in not being greedy and attempting to save the 4 Black stones.
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349
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350 <p>(Although I have characterized this as an "advanced" problem because it involved both sides
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351 playing "beneath the stones", to a strong Go player it is really quite simple and many more
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352 difficult situations are routinely encountered on a daily basis.) <a href="#Problem 4">
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353
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354 <p>Prior</a><a href="#Problem 6">
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355
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356 <p>Next</a>
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357
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358 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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359
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360 <p><hr>
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361 </font>
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362 <br wp="br1"><br wp="br2"><a name="Problem 6 Solution">
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363 <p>Problem 6 Solution</a>
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364
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365 <p><img src="img18.gif" width="122" height="142" align="left" >B1 is the key point, and after this White cannot avoid the Ko.
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366
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367 <p>W2 is forced! If this stone is mistakenly played at 3 to form an eye, the
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368 clever "throw in" sacrifice of B3 at 2 sets up a SNAPBACK which captures
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369 4 stones and kills the entire White group outright!
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370
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371 <p>If W2 correctly connects as shown, then the atari of B3 sets up a Ko in the
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372 corner when W4 makes its forced capture. This is a "flower viewing" Ko for
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373 Black because it has cost him nothing if he loses it (and even then he will
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374 almost certainly profit elsewhere as a result of the Ko threat which White
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375 can't afford to answer), while White risks his entire corner here (worth over 20 points!). <a href="#Problem 5">
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376
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377 <p>Prior</a><a href="#Problem 7">
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378
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379 <p>Next</a>
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380
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381 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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382
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383 <p><hr>
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384
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385 <br wp="br1"><br wp="br2"><a name="Problem 7 Solution">
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386 <p>Problem 7 Solution</a>
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387
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388 <p><img src="img19.gif" width="142" height="182" align="left" ><img src="img20.gif" width="142" height="182" align="left" >
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389 B1 is the only way to begin, but then W2 establishes a connection to his stones below, and it looks bad for Black!
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390
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391 <p>But B3 is a clever sacrifice which gives atari to
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392 both Whites, so W4 MUST capture it.
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393
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394 <p>Next, B5 threatens to continue at 7 with a double
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395 atari, so White MUST connect at either 6 or 8.
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396
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397 <p>Then when B7 gives atari W must make the other connection, because allowing the capture
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398 would not only give Black his needed 2 eyes but some prisoners as well.
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399
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400 <p>Finally, B9 forms the needed 2 eyes to give Black life and safety. <a href="#Problem 6">
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401
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402 <p>Prior</a><a href="#Problem 8">
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403
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404 <p>Next</a>
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405
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406 <p>Click here to return to <a href="#The Magic Of Go">The Magic Of Go</a>
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407
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408 <p><hr>
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409
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410 <br wp="br1"><br wp="br2"><a name="Problem 8 Solution">
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411 <p>Problem 8 Solution</a>
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412
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413 <p><img src="img21.gif" width="122" height="162" align="left" >The solution to this problem is provided by the Japanese Go proverb "There
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414 is death in the Hane".
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415
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416 <p>B1 is the first Hane, narrowing White's eyespace and threatening to continue
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417 at "a".
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418
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419 <p>W2 is atari on B1, while also preventing the killing B"a".
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420
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421 <p>Because of the presence of the marked Black stone, White cannot escape
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422 even if he captures B1, so B3 ignores the atari to make a second Hane on the
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423 other side, threatening to continue at "b".
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424
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425 <p>This time W4 isn't an atari so Black has time for the clever placement of B5, but with W4 White
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426 is now assured of one eye in the corner..
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427
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428 <p>Since B5 threatens to connect out at 6 to kill White's second eye, W6 is forced, but then....
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429
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430 <p>B7 is atari on two separate White 2-stone units, assuring the capture of one or the other of them.
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431
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432 <p>After this, W"c" seems to make 2 eyes after all, but is really futile because after Black captures 2
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433 Whites via B"d" or B"e", either W2 or W4 will eventually be put in atari, so the needed eye at
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434 either "a" or "b" will be false and White is dead! <a href="#Problem 7">
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435
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436 <p>Prior</a><a href="#Problem 9">
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437
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438 <p>Next</a>
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439
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440 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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441
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442 <p><hr>
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443 <a name="Problem 9 Solution">
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444 <p>Problem 9 Solution</a>
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445
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446 <p><img src="img22.gif" width="162" height="142" align="left" >B1 not only prevents a White atari at this same point while practically
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447 assuring the capture of the marked White stone, but also prepares to
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448 make an eye in the corner by continuing at 2, so...
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449
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450 <p>W2 is a sacrifice on the key point to prevent the Black eye.
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451
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452 <p>Next, B3 is a clever counter-sacrifice which does 2 key things:
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453
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454 <p>By threatening to capture the 2 Whites below, it forces W4 to assure
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455 its own capture; and until B3 IS captured White can't give atari at "a"
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456 to the 2 Blacks because it would be a self-atari!
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457
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458 <p>This gives Black time to play B5, which threatens to continue at 6 to capture 2 Whites separately
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459 and make Black's needed 2 eyes, so....
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460
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461 <p>W6 is yet another sacrifice to prevent this, allowing
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462
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463 <p>B7, which makes an eye and assures Black's life. Why? Because with "c" still open W"d" can be
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464 met by B"e" to atari and assure the capture of the 3 Whites and make Black's second eye! <a href="#Problem 8">
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465
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466 <p>Prior</a><a href="#Problem 10">
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467
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468 <p>Next</a>
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469
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470 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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471 <p><hr>
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472 <a name="Problem 10 Solution">
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473 <p>Problem 10 Solution</a>
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474
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475 <p><img src="img23.gif" width="162" height="142" align="left" >The key to the solution is the sacrifice of B1 to prevent White's own
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476 play on this key eyemaking point.
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477
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478 <p>W2 desperately tries to enlarge his eyespace, so the block of B3 is
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479 essential to contain this.
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480
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481 <p>W4 threatens to continue at 5 to form one eye and assure the capture
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482 of 2 Blacks to assure the second, so....
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483
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484 <p>The additional sacrifice of B5 to prevent this is necessary.
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485
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486 <p>Next, W6 again threatens to make an eye by continuing at 7, so yet another sacrifice via B7 on
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487 this new key point is necessary.
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488
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489 <p>Next W8 threatens to continue at "a" to assure the capture of 4 Blacks with a "live shape" for
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490 White, so...
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491
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492 <p>Yet another sacrifice via B9 is necessary to assure the death of the White group because now
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493 W"a" would capture 5 Blacks in a "dead shape". Why? Because after W"a"' captures the 5
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494 Blacks, a final Black sacrifice "beneath the stones" at 1 reduces White to 1 eye and kills. <a href="#Problem 9">
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495
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496 <p>Prior</a><a href="Legend.html">
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497
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498 <p>Click here to Return To <a href="#The Magic Of Go">The Magic Of Go</a>
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499
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500 <p><strong><a href="Legend.html"><font Color="#0033FF">Continue</font></a></strong>
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501
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502 <p>Click Here To Return To<a href="index.html"><Font Color="#0033FF"><strong> Milt's Go
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503 Page</strong></Font></a>
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504
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505 <br wp="br1"><br wp="br2">
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506 <p><hr>
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507
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508 </body>
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509
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510 <!-- Mirrored from users.eniinternet.com/bradleym/Magic.html by HTTrack Website Copier/3.x [XR&CO'2014], Sun, 06 Nov 2022 06:49:33 GMT -->
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511 </html>
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