annotate 2017/day13/problem @ 34:049fb8e56025

Add problem statements and inputs
author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Tue, 09 Jan 2018 21:51:44 -0500
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1 --- Day 13: Packet Scanners ---
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2
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3 You need to cross a vast firewall. The firewall consists of several
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4 layers, each with a security scanner that moves back and forth across
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5 the layer. To succeed, you must not be detected by a scanner.
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6
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7 By studying the firewall briefly, you are able to record (in your
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8 puzzle input) the depth of each layer and the range of the scanning
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9 area for the scanner within it, written as depth: range. Each layer
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10 has a thickness of exactly 1. A layer at depth 0 begins immediately
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11 inside the firewall; a layer at depth 1 would start immediately after
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12 that.
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13
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14 For example, suppose you've recorded the following:
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15
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16 0: 3
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17 1: 2
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18 4: 4
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19 6: 4
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20
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21 This means that there is a layer immediately inside the firewall (with
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22 range 3), a second layer immediately after that (with range 2), a
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23 third layer which begins at depth 4 (with range 4), and a fourth layer
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24 which begins at depth 6 (also with range 4). Visually, it might look
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25 like this:
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26
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27 0 1 2 3 4 5 6
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28 [ ] [ ] ... ... [ ] ... [ ]
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29 [ ] [ ] [ ] [ ]
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31 [ ] [ ]
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32
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33 Within each layer, a security scanner moves back and forth within its
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34 range. Each security scanner starts at the top and moves down until it
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35 reaches the bottom, then moves up until it reaches the top, and
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36 repeats. A security scanner takes one picosecond to move one step.
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37 Drawing scanners as S, the first few picoseconds look like this:
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38
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39
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40 Picosecond 0:
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41 0 1 2 3 4 5 6
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42 [S] [S] ... ... [S] ... [S]
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43 [ ] [ ] [ ] [ ]
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44 [ ] [ ] [ ]
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45 [ ] [ ]
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46
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47 Picosecond 1:
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48 0 1 2 3 4 5 6
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49 [ ] [ ] ... ... [ ] ... [ ]
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50 [S] [S] [S] [S]
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51 [ ] [ ] [ ]
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52 [ ] [ ]
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53
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54 Picosecond 2:
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55 0 1 2 3 4 5 6
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56 [ ] [S] ... ... [ ] ... [ ]
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57 [ ] [ ] [ ] [ ]
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58 [S] [S] [S]
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59 [ ] [ ]
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60
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61 Picosecond 3:
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62 0 1 2 3 4 5 6
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63 [ ] [ ] ... ... [ ] ... [ ]
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64 [S] [S] [ ] [ ]
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65 [ ] [ ] [ ]
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66 [S] [S]
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67
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68 Your plan is to hitch a ride on a packet about to move through the
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69 firewall. The packet will travel along the top of each layer, and it
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70 moves at one layer per picosecond. Each picosecond, the packet moves
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71 one layer forward (its first move takes it into layer 0), and then the
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72 scanners move one step. If there is a scanner at the top of the layer
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73 as your packet enters it, you are caught. (If a scanner moves into the
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74 top of its layer while you are there, you are not caught: it doesn't
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75 have time to notice you before you leave.) If you were to do this in
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76 the configuration above, marking your current position with
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77 parentheses, your passage through the firewall would look like this:
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78
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79 Initial state:
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80 0 1 2 3 4 5 6
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81 [S] [S] ... ... [S] ... [S]
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82 [ ] [ ] [ ] [ ]
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83 [ ] [ ] [ ]
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84 [ ] [ ]
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85
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86 Picosecond 0:
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87 0 1 2 3 4 5 6
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88 (S) [S] ... ... [S] ... [S]
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89 [ ] [ ] [ ] [ ]
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92
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93 0 1 2 3 4 5 6
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94 ( ) [ ] ... ... [ ] ... [ ]
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95 [S] [S] [S] [S]
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96 [ ] [ ] [ ]
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98
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99
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100 Picosecond 1:
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101 0 1 2 3 4 5 6
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102 [ ] ( ) ... ... [ ] ... [ ]
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103 [S] [S] [S] [S]
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104 [ ] [ ] [ ]
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106
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107 0 1 2 3 4 5 6
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108 [ ] (S) ... ... [ ] ... [ ]
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109 [ ] [ ] [ ] [ ]
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110 [S] [S] [S]
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111 [ ] [ ]
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112
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113
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114 Picosecond 2:
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115 0 1 2 3 4 5 6
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116 [ ] [S] (.) ... [ ] ... [ ]
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117 [ ] [ ] [ ] [ ]
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118 [S] [S] [S]
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119 [ ] [ ]
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120
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121 0 1 2 3 4 5 6
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122 [ ] [ ] (.) ... [ ] ... [ ]
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123 [S] [S] [ ] [ ]
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124 [ ] [ ] [ ]
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125 [S] [S]
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126
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127
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128 Picosecond 3:
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129 0 1 2 3 4 5 6
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130 [ ] [ ] ... (.) [ ] ... [ ]
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131 [S] [S] [ ] [ ]
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133 [S] [S]
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134
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135 0 1 2 3 4 5 6
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136 [S] [S] ... (.) [ ] ... [ ]
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138 [ ] [S] [S]
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139 [ ] [ ]
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141
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142 Picosecond 4:
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143 0 1 2 3 4 5 6
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144 [S] [S] ... ... ( ) ... [ ]
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145 [ ] [ ] [ ] [ ]
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146 [ ] [S] [S]
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147 [ ] [ ]
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148
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149 0 1 2 3 4 5 6
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150 [ ] [ ] ... ... ( ) ... [ ]
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151 [S] [S] [S] [S]
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152 [ ] [ ] [ ]
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154
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155
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156 Picosecond 5:
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157 0 1 2 3 4 5 6
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158 [ ] [ ] ... ... [ ] (.) [ ]
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159 [S] [S] [S] [S]
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160 [ ] [ ] [ ]
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161 [ ] [ ]
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162
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163 0 1 2 3 4 5 6
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164 [ ] [S] ... ... [S] (.) [S]
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165 [ ] [ ] [ ] [ ]
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166 [S] [ ] [ ]
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167 [ ] [ ]
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168
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169
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170 Picosecond 6:
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171 0 1 2 3 4 5 6
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172 [ ] [S] ... ... [S] ... (S)
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173 [ ] [ ] [ ] [ ]
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174 [S] [ ] [ ]
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175 [ ] [ ]
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176
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177 0 1 2 3 4 5 6
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178 [ ] [ ] ... ... [ ] ... ( )
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179 [S] [S] [S] [S]
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180 [ ] [ ] [ ]
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181 [ ] [ ]
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182
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183 In this situation, you are caught in layers 0 and 6, because your
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184 packet entered the layer when its scanner was at the top when you
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185 entered it. You are not caught in layer 1, since the scanner moved
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186 into the top of the layer once you were already there.
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187
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188 The severity of getting caught on a layer is equal to its depth
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189 multiplied by its range. (Ignore layers in which you do not get
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190 caught.) The severity of the whole trip is the sum of these values. In
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191 the example above, the trip severity is 0*3 + 6*4 = 24.
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192
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193 Given the details of the firewall you've recorded, if you leave
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194 immediately, what is the severity of your whole trip?
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195
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196 Your puzzle answer was 1300.
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197
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198 --- Part Two ---
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199
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200 Now, you need to pass through the firewall without being caught -
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201 easier said than done.
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202
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203 You can't control the speed of the packet, but you can delay it any
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204 number of picoseconds. For each picosecond you delay the packet before
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205 beginning your trip, all security scanners move one step. You're not
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206 in the firewall during this time; you don't enter layer 0 until you
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207 stop delaying the packet.
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208
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209 In the example above, if you delay 10 picoseconds (picoseconds 0 - 9),
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210 you won't get caught:
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211
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212 State after delaying:
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213 0 1 2 3 4 5 6
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214 [ ] [S] ... ... [ ] ... [ ]
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215 [ ] [ ] [ ] [ ]
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216 [S] [S] [S]
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217 [ ] [ ]
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218
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219 Picosecond 10:
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220 0 1 2 3 4 5 6
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221 ( ) [S] ... ... [ ] ... [ ]
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222 [ ] [ ] [ ] [ ]
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223 [S] [S] [S]
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224 [ ] [ ]
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225
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226 0 1 2 3 4 5 6
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227 ( ) [ ] ... ... [ ] ... [ ]
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228 [S] [S] [S] [S]
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229 [ ] [ ] [ ]
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230 [ ] [ ]
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231
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232
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233 Picosecond 11:
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234 0 1 2 3 4 5 6
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235 [ ] ( ) ... ... [ ] ... [ ]
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236 [S] [S] [S] [S]
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237 [ ] [ ] [ ]
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238 [ ] [ ]
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239
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240 0 1 2 3 4 5 6
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241 [S] (S) ... ... [S] ... [S]
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242 [ ] [ ] [ ] [ ]
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243 [ ] [ ] [ ]
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244 [ ] [ ]
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245
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246
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247 Picosecond 12:
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248 0 1 2 3 4 5 6
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249 [S] [S] (.) ... [S] ... [S]
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250 [ ] [ ] [ ] [ ]
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251 [ ] [ ] [ ]
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252 [ ] [ ]
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253
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254 0 1 2 3 4 5 6
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255 [ ] [ ] (.) ... [ ] ... [ ]
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256 [S] [S] [S] [S]
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257 [ ] [ ] [ ]
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258 [ ] [ ]
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259
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260
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261 Picosecond 13:
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262 0 1 2 3 4 5 6
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263 [ ] [ ] ... (.) [ ] ... [ ]
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264 [S] [S] [S] [S]
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265 [ ] [ ] [ ]
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266 [ ] [ ]
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267
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268 0 1 2 3 4 5 6
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269 [ ] [S] ... (.) [ ] ... [ ]
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270 [ ] [ ] [ ] [ ]
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271 [S] [S] [S]
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272 [ ] [ ]
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273
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274
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275 Picosecond 14:
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276 0 1 2 3 4 5 6
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277 [ ] [S] ... ... ( ) ... [ ]
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278 [ ] [ ] [ ] [ ]
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279 [S] [S] [S]
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280 [ ] [ ]
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281
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282 0 1 2 3 4 5 6
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283 [ ] [ ] ... ... ( ) ... [ ]
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284 [S] [S] [ ] [ ]
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285 [ ] [ ] [ ]
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286 [S] [S]
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287
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288
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289 Picosecond 15:
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290 0 1 2 3 4 5 6
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291 [ ] [ ] ... ... [ ] (.) [ ]
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292 [S] [S] [ ] [ ]
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293 [ ] [ ] [ ]
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294 [S] [S]
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295
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296 0 1 2 3 4 5 6
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297 [S] [S] ... ... [ ] (.) [ ]
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298 [ ] [ ] [ ] [ ]
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299 [ ] [S] [S]
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300 [ ] [ ]
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301
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302
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303 Picosecond 16:
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304 0 1 2 3 4 5 6
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305 [S] [S] ... ... [ ] ... ( )
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306 [ ] [ ] [ ] [ ]
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307 [ ] [S] [S]
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308 [ ] [ ]
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309
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310 0 1 2 3 4 5 6
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311 [ ] [ ] ... ... [ ] ... ( )
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312 [S] [S] [S] [S]
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313 [ ] [ ] [ ]
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314 [ ] [ ]
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315
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316 Because all smaller delays would get you caught, the fewest number of
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317 picoseconds you would need to delay to get through safely is 10.
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318
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319 What is the fewest number of picoseconds that you need to delay the
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320 packet to pass through the firewall without being caught?
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321
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322 Your puzzle answer was 3870382.
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323
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324 Both parts of this puzzle are complete! They provide two gold stars: **