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  1. .PL66                   INSTRUCTION╙ FO╥ FLIP
  2.  
  3.                      Numbe≥ 1║ Augus⌠ 1985
  4.  
  5.          Concept¼ Prograφ anΣ Instruction≤ b∙ Ros≤ Williams.
  6.              Fli≡ gamσ copyrigh⌠ (c⌐ Ros≤ William≤ 1982.
  7.       Prograφ anΣ Instruction≤ copyrigh⌠ (c⌐ Ros≤ William≤ 1985.
  8.                      DistributeΣ b∙ Grotniδ Software.
  9.      P.O« Bo° 372¼ Glensidσ 5065« SoutΦ Australia« Ph║ (08⌐ 7╣-2988.
  10.                         Al∞ right≤ reserved.
  11.                     GROTNI╦ i≤ ß registereΣ trademark.
  12.  
  13.  
  14. Fli≡ i≤ aε intriguinτ puzzlσ tha⌠ capture≤ thσ interes⌠ oµ almos⌠ everyonσ ì
  15. wh∩ play≤ it«  Fo≥ eacΦ ne≈ game¼ thσ playinτ boarΣ i≤ generateΣ randoml∙ ì
  16. s∩ tha⌠ eacΦ gamσ represent≤ ß ne≈ puzzle«  Simplσ ye⌠ challenging¼ Fli≡ ì
  17. present≤ ß variet∙ oµ problem≤ t∩ bσ solved.
  18.  
  19.  
  20.                         INTRODUCTION
  21.  
  22.     Congratulation≤ oε purchasinτ Flip¼ aε absorbinτ puzzlσ fo≥ thσ ì
  23. MicroBee«  I⌠ ha≤ beeε founΣ tha⌠ Fli≡ player≤ d∩ no⌠ tirσ oµ thσ gamσ ì
  24. quickl∙ a≤ i⌠ offer≤ ne≈ challenge≤ oncσ thσ basiπ gamσ i≤ mastered.
  25.  
  26.     Fli≡ i≤ ß simplσ game«  Nearl∙ al∞ oµ thσ gamσ statσ i≤ displayeΣ oε ì
  27. thσ screen«  Therσ arσ onl∙ fou≥ controls║ up¼ down¼ lef⌠ anΣ right«  Fli≡ ì
  28. i≤ suitablσ fo≥ age≤ fivσ upwards.
  29.  
  30.     Thσ gamσ i≤ s∩ simplσ tha⌠ thesσ instruction≤ arσ hardl∙ necessary«  ì
  31. However¼ therσ i≤ morσ t∩ Fli≡ thaε meet≤ thσ eyσ anΣ a≤ wel∞ a≤ containinτ ì
  32. technica∞ informatioε anΣ instruction≤ oε ho≈ t∩ pla∙ thσ game¼ thi≤ ì
  33. bookle⌠ contain≤ periphera∞ informatioε abou⌠ thσ gamσ includinτ ß partia∞ ì
  34. mathematica∞ analysis.
  35.  
  36.  
  37. Iε essence¼ though¼ Fli≡ i≤ a≤ simplσ a≤ it≤ namσ anΣ yo⌡ shoulΣ hardl∙ ì
  38. neeΣ t∩ refe≥ t∩ thesσ instructions«  T∩ ge⌠ starteΣ reaΣ thσ firs⌠ sectioε ì
  39. oε ho≈ t∩ ruε thσ game.
  40.  
  41.  
  42.                           CONTENTS
  43.  
  44.            Gettinτ Started
  45.                 1«  Runninτ Flip.....................3
  46.  
  47.            Ho≈ t∩ Pla∙ Flip
  48.                 2«  Descriptioε oµ thσ game..........3
  49.                 3«  Thσ screen.......................4
  50.                 4«  Thσ controls.....................5
  51.                 5«  Solvinτ Flip.....................6
  52.  
  53.            Note≤ oε Flip
  54.                 6«  Variation≤ oµ Flip...............8
  55.                 7«  Analysi≤ oµ Flip................10
  56. è           Appendices
  57.                 A«  Loadinτ Flip....................12
  58.                 B«  Keyma≡ fo≥ Flip.................14
  59.                 C«  Technica∞ Information...........14
  60.                 D«  Copyrigh⌠ notice................15
  61.                 E«  Acknowledgments................15
  62.  
  63.  
  64.  
  65.                  1« ╥ ╒ ╬ ╬ ╔ ╬ ╟     ╞ ╠ ╔ P
  66.  
  67.     Thi≤ sectioε i≤ designeΣ t∩ ge⌠ yo⌡ playinτ Fli≡ a≤ quickl∙ a≤ ì
  68. possible.
  69.  
  70.     Fli≡ i≤ ß machinσ codσ program« Yo⌡ wil∞ neeΣ ß MicroBeσ witΦ a⌠ leas⌠ ì
  71. 16╦ oµ memory.
  72.  
  73.     T∩ loaΣ anΣ ruε Fli≡ refe≥ t∩ Appendi° ┴ whicΦ contain≤ instruction≤ oε ì
  74. ho≈ t∩ loaΣ thσ prograφ int∩ memor∙ froφ eacΦ oµ thσ variou≤ mediß upoε ì
  75. whicΦ thσ prograφ i≤ sold.
  76.  
  77.     Iµ yo⌡ havσ correctl∙ loadeΣ anΣ ruε Flip¼ instruction≤ wil∞ appea≥ oε ì
  78. thσ screen«  ReaΣ them¼ theε pres≤ thσ RETUR╬ key«  Yo⌡ wil∞ theε bσ ì
  79. playinτ Flip.
  80.  
  81.     Thσ screeε show≤ ß fou≥ b∙ fou≥ griΣ oµ blacδ anΣ whitσ square≤ witΦ ß ì
  82. gre∙ cursor«  Thi≤ i≤ thσ puzzlσ tha⌠ yo⌡ mus⌠ solve«  B∙ movinτ thσ curso≥ ì
  83. arounΣ usinτ thσ 'W'¼ 'A'¼ 'S'¼ anΣ 'Zº keys¼ tr∙ t∩ turε thσ griΣ int∩ ì
  84. eithe≥ al∞ blacδ o≥ al∞ whitσ iε thσ minimuφ numbe≥ oµ moves.
  85.  
  86.     Iµ yo⌡ makσ ß mistake¼ ß beepinτ noisσ wil∞ bσ emitted«  Yo⌡ ma∙ finΣ ì
  87. thσ keyma≡ iε Appendi° ┬ helpful«  Iµ yo⌡ neeΣ t∩ rσ-reaΣ thσ instructions¼ ì
  88. typσ I.
  89.  
  90.  
  91.         ─ ┼ ╙ ├ ╥ ╔ ╨ ╘ ╔ ╧ ╬   ╧  ╞   ╘ ╚ ┼   ╟ ┴ ═ E
  92.  
  93.     Fli≡ i≤ ß boardgame« Thσ boarΣ consist≤ oµ sixteeε square≤ arrangeΣ iε ì
  94. ß fou≥ b∙ fou≥ grid«  A⌠ an∙ time¼ eacΦ squarσ oε thσ griΣ caε bσ coloureΣ ì
  95. eithe≥ blacδ o≥ white.
  96.  
  97.     EacΦ gamσ begin≤ witΦ ß randoml∙ coloureΣ grid«  Thσ aiφ oµ thσ gamσ i≤ ì
  98. t∩ conver⌠ thσ griΣ t∩ eithe≥ al∞ blacδ o≥ al∞ white«  Durinτ thσ game¼ yo⌡ ì
  99. caε changσ you≥ objectivσ oµ al∞ blacδ o≥ al∞ whitσ a≤ man∙ time≤ a≤ yo⌡ ì
  100. likσ anΣ wheneve≥ yo⌡ please.
  101.  
  102.     Sittinτ oε onσ oµ thσ square≤ oε thσ boarΣ i≤ ß curso≥ ove≥ whicΦ thσ ì
  103. playe≥ ha≤ control«  Thσ curso≥ caε bσ moveΣ onσ squarσ up¼ down¼ lef⌠ o≥ ì
  104. righ⌠ bu⌠ no⌠ diagonall∙ o≥ ofµ thσ board«  Aε additiona∞ restrain⌠ i≤ tha⌠ ì
  105. thσ curso≥ caε no⌠ bσ moveΣ ont∩ thσ squarσ froφ whicΦ i⌠ jus⌠ came«  Wheε ì
  106. thσ curso≥ move≤ ont∩ ß squarσ i⌠ change≤ (o≥ flips⌐ thσ colou≥ oµ thσ ì
  107. square«  I⌠ i≤ b∙ thi≤ mechanisφ tha⌠ thσ boarΣ i≤ manipulateΣ b∙ thσ ì
  108. player.
  109.  
  110.     Thesσ arσ thσ rule≤ oµ thσ gamσ Flip«  Thi≤ MicroBeσ compute≥-gamσ ìèversioε oµ Fli≡ project≤ thσ boarΣ ont∩ thσ screeε anΣ allow≤ yo⌡ t∩ movσ ì
  111. thσ curso≥ b∙ pressinτ keys«  Iµ yo⌡ makσ thσ griΣ al∞ onσ colour¼ thσ ì
  112. compute≥ wil∞ instantl∙ recognisσ tha⌠ yo⌡ havσ woε anΣ tel∞ yo⌡ ho≈ man∙ ì
  113. move≤ yo⌡ tooδ t∩ win.
  114.  
  115.  
  116.  
  117.                   3« ╘ ╚ ┼   ╙ ├ ╥ ┼ ┼ N
  118.  
  119.  
  120.     Thi≤ sectioε describe≤ thσ informatioε tha⌠ i≤ projecteΣ ont∩ thσ ì
  121. computer'≤ screeε durinτ thσ gamσ oµ Flip«  A≤ wel∞ a≤ representinτ thσ ì
  122. gameboard¼ thσ screeε contain≤ somσ helpfu∞ reminde≥ informatioε anΣ thσ ì
  123. statu≤ oµ thσ sounΣ anΣ joysticδ options«  Herσ i≤ aε annotateΣ diagraφ oµ ì
  124. thσ screeε durinτ thσ gamσ oµ Flip.
  125.  
  126.         Cursor
  127.  
  128. ½¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡-+
  129. :½¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡-½   ┼  :╝¡-Thσ word
  130. :║          ║           :///////////://////////║   ╥  ║   ERROR
  131. :║   O╧     ║           :///////////://////////║   ╥  ║   flashes
  132. :║   O╧     ║           :///////////://////////║   ╧  ║   herσ if
  133. :║          ║           :///////////://////////║   ╥  ║   yo⌡ makσ a
  134. :║          ║           :///////////://////////║      ║   mistake.
  135. :½¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡-½      :
  136. :://////////║           ║           ║          ║      :
  137. :://////////║           ║           ║          ║  ES├ :╝¡-Helpfu∞ 
  138. :://////////║           ║           ║          ║      ║   notσ of
  139. :://////////║           ║           ║          ║      ║   ke∙ t∩ end
  140. :://////////║           ║           ║          ║      ║   thσ game.
  141. :½¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡-½      :
  142. :║          ║           :///////////║          ║  ╫   :╝¡-Helpful
  143. :║          ║           :///////////║          ║ ┴ ╙  ║   notσ of
  144. :║          ║           :///////////║          ║  ┌   ║   key≤ to
  145. :║          ║           :///////////║          ║      ║   move.
  146. :║          ║           :///////////║          ║      :
  147. :½¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡-½      :
  148. :║          ║           ║           ║          ║      :
  149. :║          ║           ║           ║          ║  █   :╝¡-Helpful
  150. :║          ║           ║           ║          ║ ╗ └  ║   notσ of
  151. :║          ║           ║           ║          ║  »   ║   key≤ to
  152. :║          ║           ║           ║          ║      ║   move.
  153. :½¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡¡-½¡¡¡¡¡¡¡¡¡-½      :
  154. :Pres≤ ▒ fo≥ instructions«                            :
  155. ║    ⁿ    N∩ sound[G▌ N∩ Joystick[J▌ Moves:░          :
  156. ½¡¡¡-ⁿ¡¡¡¡¡¡¡-ⁿ¡¡¡¡¡¡¡¡¡¡¡-ⁿ¡¡¡¡¡¡¡¡¡¡¡¡¡-ⁿ¡¡¡¡¡¡¡¡¡¡-+
  157. Helpfu∞   SounΣ statu≤   Joysticδ      Thσ number
  158. reminde≥  'Noº mean≤     statu≤        oµ move≤ you
  159. message«  silence;'º     'Noº mean≤    havσ madσ s∩ far.
  160.           mean≤ beeps«   disabled╗  
  161.           Pres≤ ╟ t∩     'º mean≤ enabled.
  162.           change«        Pres≤ ╩ t∩ change.
  163.  
  164. è    Thσ square≤ oε thσ screeε arσ thσ gamσ squares« Thσ gre∙ squarσ tha⌠ ì
  165. appear≤ iε onσ oµ thσ gamσ square≤ i≤ thσ curso≥ tha⌠ i≤ useΣ t∩ movσ ì
  166. arounΣ thσ boarΣ anΣ fli≡ thσ squares.
  167.  
  168.     Thσ 'Pres≤ ╔ fo≥ Instructionsº tha⌠ appear≤ a⌠ thσ bottoφ oµ thσ screeε ì
  169. i≤ n∩ morσ thaε ß reminde≥ tha⌠ thσ instructioε pagσ i≤ instantl∙ ì
  170. accessiblσ b∙ pressinτ thσ ╔ key.
  171.  
  172.     Thσ worΣ 'Soundº a⌠ thσ bottoφ oµ thσ screeε display≤ whethe≥ sounΣ i≤ ì
  173. enabled«  SounΣ refer≤ t∩ thσ beepinτ noisσ tha⌠ i≤ emitteΣ iµ ß mistakσ i≤ ì
  174. made« Iµ sounΣ i≤ turneΣ off¼ ß 'Noº wil∞ appea≥ beforσ thσ worΣ 'Soundº ì
  175. readinτ 'N∩ Sound'«  Iµ sounΣ i≤ turneΣ on¼ thσ 'Noº wil∞ bσ absen⌠ anΣ ì
  176. jus⌠ thσ worΣ 'Soundº wil∞ bσ visible«  Thσ '[G]º i≤ t∩ reminΣ yo⌡ tha⌠ t∩ ì
  177. togglσ thσ sounΣ status¼ yo⌡ neeΣ t∩ pres≤ thσ ╟ key.
  178.  
  179.     Thσ worΣ 'Joystickº a⌠ thσ bottoφ oµ thσ screeε display≤ whethe≥ thσ ì
  180. joysticδ facilit∙ i≤ enabled«  Iµ i⌠ isn'⌠ theε ß 'Noº wil∞ appea≥ beforσ ì
  181. thσ worΣ 'Joystickº readinτ 'N∩ Joystick'«  Iµ thσ joysticδ facilit∙ i≤ ì
  182. enabled¼ thσ 'Noº wil∞ bσ absen⌠ anΣ jus⌠ thσ worΣ 'Joystickº wil∞ bσ ì
  183. visible«  Thσ '[J]º i≤ t∩ reminΣ yo⌡ tha⌠ t∩ togglσ thσ joysticδ status¼ ì
  184. yo⌡ wil∞ neeΣ t∩ pres≤ thσ ╩ key.
  185.  
  186.     Thσ numbe≥ oµ move≤ tha⌠ yo⌡ havσ madσ sincσ thσ gamσ starteΣ i≤ ì
  187. displayeΣ afte≥ thσ worΣ 'Movesº iε thσ bottoφ righ⌠ corner«  EacΦ timσ thσ ì
  188. curso≥ i≤ moveΣ froφ onσ squarσ t∩ thσ next¼ thσ move≤ coun⌠ i≤ incrementeΣ ì
  189. b∙ one.
  190.  
  191.     A≤ ß reminde≥ oµ thσ key≤ tha⌠ contro∞ thσ cursor¼ thσ ke∙ label≤ fo≥ ì
  192. eacΦ oµ thσ tw∩ directiona∞ ke∙ set≤ arσ displayeΣ t∩ thσ righ⌠ oµ thσ ì
  193. grid«  Thu≤ 'Wº i≤ up¼ 'Aº i≤ left¼ anΣ s∩ on« ES├ sit≤ oε it≤ owε a≤ ß ì
  194. reminde≥ tha⌠ t∩ abor⌠ thσ game¼ yo⌡ mus⌠ pres≤ ESCape.
  195.  
  196.  
  197.                 4« ╘ ╚ ┼   ├ ╧ ╬ ╘ ╥ ╧ ╠ S
  198.  
  199.     Havinτ examineΣ thσ gamσ anΣ thσ wa∙ tha⌠ i⌠ i≤ projecteΣ ont∩ thσ ì
  200. screen¼ wσ no≈ discus≤ thσ control≤ useΣ t∩ pla∙ it«  Appendi° ┬ contain≤ ß ì
  201. keyma≡ tha⌠ yo⌡ ma∙ finΣ helpfu∞ t∩ refe≥ t∩ whilσ readinτ thi≤ section.
  202.  
  203.  
  204. KEYIN╟ ERRORS
  205.  
  206.     Onl∙ ß fe≈ oµ thσ key≤ oε thσ keyboarΣ arσ valiΣ anΣ havσ ß usefu∞ ì
  207. effect«  Pressinτ onσ oµ thσ othe≥ key≤ wil∞ resul⌠ iε ß higΦ pitcheΣ ì
  208. beepinτ noisσ anΣ thσ worΣ 'ERRORº wil∞ bσ flasheΣ oε thσ righ⌠ hanΣ sidσ ì
  209. oµ thσ screeε t∩ indicatσ you≥ mistake.
  210.  
  211.  
  212. HELP
  213.  
  214.     A⌠ an∙ timσ durinτ thσ game¼ yo⌡ caε revie≈ thσ rule≤ oµ Fli≡ b∙ ì
  215. pressinτ I«  Iµ thi≤ i≤ done¼ thσ instruction≤ screeε wil∞ bσ displayeΣ anΣ ì
  216. afte≥ yo⌡ havσ finisheΣ witΦ it¼ yo⌡ caε returε t∩ you≥ gamσ b∙ pressinτ ì
  217. RETURN.
  218. èMOVIN╟ TH┼ CURSOR
  219.  
  220.     Therσ arσ tw∩ set≤ oµ control≤ fo≥ movinτ thσ cursor«  Thesσ arσ thσ ì
  221. 'Wº-up¼ 'Aº-left¼ 'Sº-righ⌠ anΣ 'Zº-dowε key≤ anΣ thσ '[º-up¼ ';º-left¼ ì
  222. '@º-righ⌠ anΣ '/º-dowε keys«  Wheε yo⌡ pres≤ ß movemen⌠ key¼ tw∩ thing≤ caε ì
  223. happen«  Iµ yo⌡ havσ attempteΣ ß valiΣ move¼ thσ curso≥ wil∞ movσ iε thσ ì
  224. directioε oµ thσ command«  Iµ yo⌡ havσ attempteΣ aε invaliΣ movσ theε thσ ì
  225. curso≥ wil∞ no⌠ movσ anΣ ß lo≈ pitcheΣ beepinτ noisσ wil∞ sounΣ t∩ indicatσ ì
  226. you≥ mistake«  Thσ worΣ 'ERRORº wil∞ als∩ bσ flasheΣ oε thσ righ⌠ hanΣ sidσ ì
  227. oµ thσ screen«  ┴ movσ i≤ invaliΣ iµ i⌠ woulΣ movσ thσ curso≥ ont∩ thσ ì
  228. squarσ froφ whicΦ i⌠ jus⌠ came.
  229.  
  230.  
  231. JOYSTIC╦ CONTROL
  232.  
  233.     Fli≡ ma∙ bσ playeΣ usinτ ß standarΣ MicroBeσ joysticδ a≤ describeΣ iε ì
  234. thσ Testinτ You≥ Joystickü articlσ oµ thσ MicroBeσ Engineerinτ Notebookü ì
  235. publisheΣ b∙ ApplieΣ Technology«  T∩ pla∙ Fli≡ usinτ ß Joystick¼ connec⌠ ì
  236. thσ joysticδ t∩ thσ MicroBee«  Yo⌡ mus⌠ theε enablσ joysticδ contro∞ iε ì
  237. Fli≡ b∙ pressinτ thσ 'Jº key«  Pressinτ 'Jº toggle≤ joysticδ enabling«  ì
  238. Durinτ ß game¼ yo⌡ caε seσ whethe≥ thσ joysticδ i≤ currentl∙ enableΣ b∙ ì
  239. lookinτ a⌠ thσ joysticδ statu≤ a⌠ thσ bottoφ oµ thσ screen«  Fli≡ see≤ thσ ì
  240. joysticδ (wheε i⌠ i≤ enabled⌐ a≤ anothe≥ cop∙ oµ thσ movemen⌠ keys«  A≤ ß ì
  241. hand∙ bonus¼ Fli≡ see≤ thσ firσ buttoε a≤ ß cop∙ oµ thσ RETUR╬ key«  Thi≤ ì
  242. mean≤ tha⌠ wheε yo⌡ havσ finisheΣ ß gamσ usinτ thσ joystick¼ yo⌡ caε g∩ ì
  243. ont∩ thσ nex⌠ onσ b∙ pressinτ thσ firσ button.
  244.  
  245.  
  246. SOUND
  247.  
  248.     Thσ beepinτ noise≤ tha⌠ Fli≡ use≤ t∩ le⌠ yo⌡ kno≈ tha⌠ wheε yo⌡ havσ ì
  249. presseΣ aε incorrec⌠ ke∙ arσ generall∙ helpful«  Therσ arσ times¼ however¼ ì
  250. wheε yo⌡ ma∙ wisΦ t∩ pla∙ Fli≡ quietl∙ s∩ a≤ no⌠ t∩ disturΓ others«  ┴ ì
  251. facilit∙ ha≤ thereforσ beeε addeΣ tha⌠ allow≤ yo⌡ t∩ switcΦ thσ sounΣ oε ì
  252. anΣ off«  T∩ turε thσ sounΣ ofµ pres≤ thσ 'Gº key«  T∩ turε thσ sounΣ oε ì
  253. agaiε pres≤ i⌠ again«  Turninτ thσ beep≤ ofµ doe≤ no⌠ turε ofµ thσ worΣ ì
  254. 'ERRORº tha⌠ flashe≤ a⌠ thσ righ⌠ oµ thσ screeε s∩ yo⌡ wil∞ stil∞ bσ ì
  255. alerteΣ wheε yo⌡ makσ mistakes«  A⌠ al∞ times¼ thσ statu≤ oµ thσ sounΣ ì
  256. facilit∙ i≤ displayeΣ a⌠ thσ bottoφ oµ thσ screen.
  257.  
  258.  
  259. ABORTIN╟ ┴ GAME
  260.  
  261.     Iµ yo⌡ wisΦ t∩ abor⌠ ß game¼ pres≤ ESCape«  Yo⌡ wil∞ theε bσ prompteΣ ì
  262. anΣ havσ thσ optioε oµ eithe≥ playinτ anothe≥ gamσ o≥ exitinτ thσ program.
  263.  
  264.  
  265. WINNING
  266.  
  267.     Iε MicroBeσ Flip¼ yo⌡ d∩ no⌠ neeΣ t∩ declarσ t∩ thσ compute≥ iε an∙ wa∙ ì
  268. tha⌠ yo⌡ havσ won«  Afte≥ ever∙ movσ tha⌠ yo⌡ make¼ thσ compute≥ check≤ thσ ì
  269. boarΣ anΣ iµ yo⌡ havσ won¼ i⌠ place≤ ß winninτ messagσ u≡ anΣ ask≤ yo⌡ iµ ì
  270. yo⌡ wan⌠ anothe≥ game.
  271.  
  272. è                     ╙ ╧ ╠ ╓ ╔ ╬ ╟    ╞ ╠ ╔ P
  273.  
  274.     Thi≤ sectioε outline≤ ß methoΣ fo≥ solvinτ Fli≡ tha⌠ thσ autho≥ ha≤ ì
  275. realizeΣ hσ i≤ usinτ wheε solvinτ Flip«  Thσ methoΣ i≤ no⌠ ß rigorou≤ ste≡ ì
  276. b∙ ste≡ solutioε bu⌠ rathe≥ ß genera∞ outlinσ oµ ho≈ t∩ g∩ abou⌠ playinτ ì
  277. thσ game«  Iµ yo⌡ arσ havinτ troublσ solvinτ Flip¼ yo⌡ migh⌠ finΣ thi≤ ì
  278. sectioε helpful«  Iµ yo⌡ aren't¼ yo⌡ migh⌠ finΣ thi≤ sectioε interesting¼ ì
  279. a≤ thσ technique≤ expresseΣ herσ ma∙ bσ wha⌠ yo⌡ arσ doinτ intuitivel∙ ì
  280. anyway!
  281.  
  282.     ┴ probleφ divideΣ i≤ ß probleφ lessened«  Solvinτ Fli≡ caε bσ vieweΣ a≤ ì
  283. ß tw∩ stagσ process«  Durinτ an∙ gamσ oµ Flip¼ therσ i≤ ß poin⌠ iε thσ gamσ ì
  284. wherσ yo⌡ caε suddenl∙ seσ thσ wa∙ t∩ finish«  BoarΣ configuration≤ wherσ ì
  285. thi≤ happen≤ fo≥ yo⌡ wσ shal∞ cal∞ watersheΣ configurations«  Finishinτ ofµ ì
  286. thσ gamσ afte≥ thi≤ poin⌠ i≤ stagσ two«  Thσ proces≤ oµ fiddlinτ arounΣ t∩ ì
  287. ge⌠ t∩ thσ watersheΣ configuratioε i≤ stagσ one.
  288.  
  289.     Whilσ thi≤ ma∙ no⌠ seeφ aε astonishinτ observation¼ i⌠ i≤ usefu∞ ì
  290. becausσ thσ se⌠ oµ gamσ configuration≤ tha⌠ tenΣ t∩ forφ thσ watersheΣ ì
  291. configuratioε caε bσ characteriseΣ anΣ aε intuitivσ sensσ fo≥ thesσ ì
  292. formation≤ caε bσ developed«  Oncσ thi≤ i≤ done¼ thσ probleφ i≤ spli⌠ iε ì
  293. half«  T∩ finisΦ ß game¼ yo⌡ firs⌠ movσ arounΣ usinτ intuitioε t∩ ge⌠ t∩ ß ì
  294. watersheΣ configuration«  Afte≥ tha⌠ thσ solutioε i≤ obviou≤ b∙ definition«  ì
  295. Thσ cru° oµ thi≤ methoΣ i≤ identifyinτ anΣ workinτ toward≤ thσ watersheΣ ì
  296. configurations«  Firs⌠ thσ identification.
  297.  
  298.     WatersheΣ configuration≤ arσ characteriseΣ b∙ thσ playe≥ beinτ ablσ t∩ ì
  299. seσ ß solutioε easil∙ froφ tha⌠ point«  Naturall∙ morσ experienceΣ player≤ ì
  300. wil∞ havσ morσ watersheΣ configuration≤ thaε novices«  Fo≥ thσ perfec⌠ ì
  301. player¼ ever∙ boarΣ configuratioε i≤ ß watersheΣ configurationí  Wσ shal∞ ì
  302. dea∞ witΦ onl∙ easil∙ recognisablσ watersheΣ configurations.
  303.  
  304.     Configuration≤ whosσ solution≤ arσ easil∙ recogniseΣ arσ usuall∙ ì
  305. characteriseΣ b∙ ß clea≥ mappinτ oµ thσ configuratioε presenteΣ t∩ thσ ì
  306. playe≥ t∩ thσ sequencσ oµ move≤ tha⌠ wil∞ completσ thσ game«  Herσ arσ somσ ì
  307. examples:
  308.  
  309.  
  310.      ╧ represent≤ inverteΣ square.
  311.  
  312. ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-+
  313. :___:__:__:__║  :___:__:__:__║  :O__:O_:O_:__║  :O__:O_:O_:O_:
  314. :___:O_:<_:__║  :___:__:v_:__║  :O__:O_:O_:__║  :O__:>_:O_:O_:
  315. :___:__:__:__║  :___:__:O_:O_║  :___:^_:__:__║  :O__:__:O_:__:
  316. :___:__:__:__║  :___:__:O_:O_║  :___:__:__:__║  :O__:O_:O_:__:
  317.  
  318. ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-+
  319. :O__:O_:O_:O_║  :___:__:__:__║  :O__:O_:__:__║  :___:__:O_:O_:
  320. :O__:O_:O_:__║  :___:O_:O_:O_║  :O__:v_:__:__║  :O__:O_:O_:O_:
  321. :___:__:O_:__║  :___:O_:O_:O_║  :O__:O_:__:__║  :O__:O_:__:O_:
  322. :>__:O_:O_:__║  :___:>_:O_:O_║  :O__:O_:__:__║  :___:>_:O_:O_:
  323.  
  324.  
  325.  
  326. 轡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-+
  327. :___:O_:O_:O_║  :O__:O_:O_:O_║  :___:O_:O_:O_║  :___:O_:O_:O_:
  328. :O__:O_:O_:O_║  :O__:O_:O_:O_║  :___:O_:O_:O_║  :___:O_:__:O_:
  329. :___:__:^_:__║  :O__:^_:__:O_║  :O__:O_:O_:O_║  :___:O_:O_:O_:
  330. :___:__:__:__║  :O__:O_:O_:O_║  :^__:__:O_:O_║  :___:__:__:^_:
  331.  
  332.  
  333.     Yo⌡ havσ probabl∙ noticeΣ tha⌠ ß gooΣ rulσ fo≥ characterisinτ watersheΣ ì
  334. configuration≤ is║ "Al∞ thosσ configuration≤ tha⌠ caε bσ solveΣ withou⌠ thσ ì
  335. curso≥ havinτ t∩ cros≤ it≤ owε path.ó  Thi≤ rulσ arise≤ becausσ wherσ ß ì
  336. solutioε patΦ exist≤ unde≥ thσ abovσ condition¼ i⌠ i≤ virtuall∙ drawε oε ì
  337. thσ screen!í  Solutioε path≤ exis⌠ tha⌠ cros≤ thei≥ owε patΦ bu⌠ the∙ d∩ ì
  338. no⌠ ma≡ themselve≤ clearl∙ anΣ simpl∙ ont∩ thσ board«  Rathe≥ the∙ obscurσ ì
  339. an∙ possiblσ visua∞ mappinτ b∙ runninτ ove≥ themselves«  Herσ arσ tw∩ ì
  340. example≤ oµ unfriendl∙ configuration≤ anΣ thei≥ simplσ solutions.
  341.  
  342. ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-+
  343. :O__:__:__:__║  :_v_:<_:__:__║  :O__:__:O_:__║  :_>_:v>:v_:__:
  344. :O__:__:__:__:╜ :_>_:^^:__:__║  :O__:O_:O_:__║  :_^_:_^:<_:__:
  345. :___:^_:__:__║  :___:_^:__:__║  :___:O_:__:__║  :___:_^:__:__:
  346. :___:__:__:__║  :___:__:__:__║  :___:^_:__:__║  :___:_^:__:__:
  347.  
  348.  
  349.     Thσ wa∙ froφ thσ curren⌠ configuratioε t∩ ß watersheΣ configuratioε i≤ ì
  350. usuall∙ no⌠ obvious«  However¼ i⌠ i≤ usuall∙ fa≥ morσ obviou≤ thaε thσ wa∙ ì
  351. t∩ ß solutioε a≤ therσ arσ fa≥ morσ watersheΣ configuration≤ tha⌠ therσ arσ ì
  352. solutioε configurations«  A≤ yo⌡ menta∞ dictionar∙ oµ watersheΣ ì
  353. configuration≤ grows¼ yo⌡ wil∞ finΣ theφ easie≥ t∩ find«  Thσ bes⌠ wa∙ t∩ ì
  354. worδ toward≤ ß watersheΣ configuratioε i≤ t∩ looδ a⌠ thσ patterε anΣ heaΣ ì
  355. toward≤ thσ square≤ tha⌠ looδ someho≈ ou⌠ oµ place«  Failinτ this¼ jus⌠ ì
  356. wande≥ arounΣ unti∞ somethinτ hopefu∞ come≤ ou⌠ oµ thσ mess!
  357.  
  358.     Afte≥ ß whilσ yo⌡ ma∙ finΣ tha⌠ somσ watersheΣ configuration≤ appea≥ s∩ ì
  359. ofteε tha⌠ the∙ becomσ ingraineΣ anΣ seconΣ nature«  Yo⌡ wil∞ theε finΣ ì
  360. yourselµ headinτ toward≤ theφ quickl∙ anΣ intuitively«  Herσ arσ somσ ì
  361. examplσ Fli≡ boarΣ configuration≤ a⌠ thσ star⌠ oµ thσ game«  Thσ cursor¼ ì
  362. whicΦ i≤ no⌠ shown¼ i≤ iε thσ to≡ lef⌠ corne≥ anΣ caε movσ eithe≥ dowε o≥ ì
  363. right«  BeneatΦ eacΦ configuratioε i≤ thσ sequencσ oµ move≤ requireΣ t∩ ì
  364. reacΦ ß simplσ watersheΣ configuration.
  365.  
  366. ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-+
  367. :O__:O_:__:O_║  :___:__:O_:O_║  :___:__:__:__║  :___:__:O_:__:
  368. :___:__:O_:O_║  :O__:O_:__:__║  :___:O_:O_:O_║  :___:O_:O_:__:
  369. :___:__:O_:O_║  :O__:__:__:O_║  :___:O_:O_:__║  :___:__:O_:__:
  370. :___:__:__:__║  :O__:__:__:O_║  :___:O_:O_:__║  :___:O_:O_:__:
  371.   ╓  ╛            ╓  ╛              ╛   ╛   ╛     ╓  ╓   >
  372.   
  373. ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-½  ½¡¡¡¡¡¡¡¡¡¡¡-+
  374. :___:__:O_:__║  :O__:__:O_:O_║  :O__:O_:__:O_║  :O__:O_:__:__:
  375. :___:__:O_:__║  :___:__:O_:O_║  :___:O_:__:O_║  :O__:O_:__:__:
  376. :O__:O_:O_:__║  :___:O_:O_:O_║  :___:__:O_:__║  :___:__:O_:O_:
  377. :O__:O_:O_:__║  :O__:O_:O_:__║  :O__:O_:__:__║  :O__:__:O_:O_:
  378.     ╛ ╓ ╝   ▐       ╛ ╓ ╝  ╓      ╓  ╓   ╛   ╛   ╛ ╓ ╝ ▐ ╛ ╓ ╝   
  379.                                                     ╓   >╓   
  380. è    Thi≤ i≤ onσ wa∙ oµ goinτ abou⌠ solvinτ Flip«  Therσ arσ many¼ man∙ ì
  381. littlσ tricks¼ pattern≤ anΣ way≤ oµ goinτ abou⌠ solvinτ thσ gamσ tha⌠ coulΣ ì
  382. bσ listed«  ┴ rathe≥ obviou≤ examplσ i≤ thσ kee≡ aε eyσ ou⌠ fo≥ solution≤ ì
  383. iε botΦ colours«  T∩ cataloguσ al∞ thσ trick≤ woulΣ takσ fa≥ to∩ mucΦ ì
  384. space«  Hopefully¼ thσ methoΣ describeΣ ha≤ alread∙ helpeΣ yo⌡ becomσ ß ì
  385. bette≥ player.
  386.  
  387.  
  388.            6« ╓ ┴ ╥ ╔ ┴ ╘ ╔ ╧ ╬ ╙   ╧ ╞   ╞ ╠ ╔ P
  389.  
  390.     Fo≥ thσ purpose≤ oµ generalizatioε thi≤ sectioε describe≤  thσ ì
  391. generalization≤ oµ thσ gamσ Flip«  First¼ thσ origina∞ gamσ whicΦ take≤ thσ ì
  392. namσ "Flipó i≤ described«  Theε eacΦ variatioε upoε thσ gamσ i≤ describeΣ ì
  393. iε thσ forφ oµ ß variatioε oµ Flip«  Thi≤ doe≤ no⌠ meaε tha⌠ thσ variation≤ ì
  394. arσ mutuall∙ exclusive«  Mos⌠ oµ thσ variation≤ arσ orthogona∞ t∩ thσ othe≥ ì
  395. variation≤ anΣ ma∙ bσ combineΣ t∩ forφ ne≈ kind≤ oµ Flip«  Afte≥ thσ ì
  396. variations¼ tw∩ combination≤ arσ described«  Purσ Fli≡ arosσ durinτ ì
  397. analysi≤ a≤ thσ cleanes⌠ forφ oµ thσ basiπ Fli≡ game«  I⌠ i≤ ß combinatioε ì
  398. oµ Fastidiou≤ Fli≡ anΣ Firσ Flip(1)«  Supe≥ Fli≡ i≤ Fli≡ witΦ al∞ ì
  399. variation≤ included.
  400.  
  401.     Al∞ oµ thσ game≤ tha⌠ coulΣ bσ generateΣ b∙ thesσ variation≤ o≥ an∙ ì
  402. combinatioε oµ theφ arσ copyrigh⌠ (c⌐ Ros≤ William≤ 198╡ excep⌠ Fli≡ whicΦ ì
  403. i≤ ß copyrigh⌠ (c⌐ Ros≤ William≤ 1982«  Unles≤ otherwisσ stated¼ al∞ ì
  404. parameter≤ oµ thσ game≤ (eg║ N⌐ iε thσ followinτ description≤ arσ natura∞ ì
  405. number≤ (ie║ 1¼ 2¼ 3¼ 4¼ .....).
  406.  
  407.  
  408. FLIP
  409.  
  410.     Fli≡ i≤ ß gamσ fo≥ onσ playe≥ tha⌠ i≤ playeΣ oε ß 4x┤ grid«  A⌠ an∙ ì
  411. time¼ eacΦ squarσ oε thσ griΣ i≤ coloureΣ onσ oµ tw∩ colours«  EacΦ gamσ ì
  412. begin≤ witΦ ß  randoml∙ coloureΣ griΣ anΣ s∩ present≤ ß ne≈ puzzle.
  413.  
  414.     Thσ aiφ oµ thσ gamσ i≤ t∩ conver⌠ al∞ thσ square≤ t∩ thσ samσ colour«  ì
  415. Thi≤ i≤ donσ b∙ movinτ ß curso≥ froφ thσ squarσ tha⌠ i⌠ i≤ oε t∩ aε ì
  416. adjacen⌠ square«  EacΦ gamσ start≤ witΦ thσ curso≥ iε thσ to≡ lef⌠ corne≥ ì
  417. anΣ beinτ ablσ t∩ movσ dowε o≥ right«  Wheneve≥ thσ curso≥ move≤ oε t∩ ß ì
  418. square¼ i⌠ change≤ (ie║ flips⌐ thσ colou≥ oµ thσ squarσ anΣ thi≤ count≤ a≤ ì
  419. onσ move.
  420.  
  421.     Thσ curso≥ canno⌠ move:
  422.         ¬ Ou⌠ oµ thσ sixteeε squares.
  423.         ¬ Diagonally.
  424.         ¬ Oε t∩ thσ squarσ froφ whicΦ i⌠ came.
  425.  
  426.  
  427.  
  428.  
  429. VARYIN╟ TH┼ GRI─ SIZE║ ═ B┘ ╬ FLIP
  430.  
  431.     ═ b∙ ╬ Fli≡ i≤ identica∞ t∩ Fli≡ excep⌠ tha⌠ thσ boarΣ ha≤ ß heigh⌠ oµ ì
  432. ═ anΣ ß widtΦ oµ N.
  433.  
  434.     Thi≤ i≤ thσ samσ a≤ Fli≡ excep⌠ tha⌠ therσ arσ ─ dimension≤ insteaΣ oµ ìètw∩ dimensions«  Thσ "n∩ diagona∞ movesó rulσ become≤ thσ "thσ curso≥ ma∙ ì
  435. onl∙ movσ iε onσ dimensioε iε eacΦ move".
  436.  
  437. VARYIN╟ TH┼ NUMBE╥ O╞ COLOURS║ MULTICOLOU╥ FLIP
  438.  
  439.     Multicolou≥ Fli≡ i≤ identica∞ t∩ Fli≡ excep⌠ tha⌠ eacΦ squarσ ma∙ bσ ì
  440. onσ oµ ╙ colours«  EacΦ square¼ rathe≥ thaε beinτ imagineΣ a≤ ß platσ witΦ ì
  441. onσ colou≥ oε eacΦ side¼ mus⌠ bσ imagineΣ a≤ ß druφ witΦ ╙ face≤ tha⌠ i≤ ì
  442. rotateΣ onσ facσ wheε thσ curso≥ land≤ oε it.
  443.  
  444. VARYIN╟ TH┼ NUMBE╥ O╞ CURSORS║ CONCURREN╘ FLIP
  445.  
  446.     Concurren⌠ Fli≡ i≤ thσ samσ a≤ Fli≡ excep⌠ tha⌠ therσ ma∙ bσ morσ thaε ì
  447. onσ cursor«  EacΦ move¼ thσ playe≥ mus⌠ choosσ ß singlσ curso≥ anΣ theε ì
  448. movσ it«  Thσ "n∩ movinτ backwardsó rulσ i≤ enforceΣ oε ß curso≥ b∙ curso≥ ì
  449. basis«  Tha⌠ is¼ an∙ onσ curso≥ ma∙ no⌠ movσ t∩ thσ squarσ froφ whicΦ i⌠ ì
  450. las⌠ came¼ regardles≤ oµ an∙ interveninτ activit∙ oµ thσ othe≥ cursors.
  451.  
  452. VARYIN╟ SQUAR┼ CONNECTIONS║ STRING┘ FLIP
  453.  
  454.     Iε string∙ Flip¼ thσ rectangula≥ structurσ oµ Fli≡ i≤ abandoned«  ì
  455. InsteaΣ oµ square≤ therσ i≤ ß directeΣ grapΦ structurσ consistinτ oµ ß ì
  456. collectioε oµ node≤ Nπ wherσ π range≤ froφ ▒ t∩ T«  EacΦ nodσ π i≤ ì
  457. connecteΣ viß ß unidirectiona∞ linδ t∩ Rc¼ ß noε-stric⌠ subse⌠ oµ thσ se⌠ ì
  458. oµ nodes«  Thσ naturσ oµ thσ connection≤ i≤ u≡ t∩ thσ instantiato≥ oµ thσ ì
  459. game.
  460.  
  461. VARYIN╟ TH┼ SOLUTIO╬ PATTERN║ FASTIDIOU╙ FLIP
  462.  
  463.     Iε Fastidiou≤ Flip¼ thσ onl∙ solutioε statσ i≤ tha⌠ iε whicΦ thσ boarΣ ì
  464. i≤ al∞ oµ thσ firs⌠ colour¼ no⌠ eithe≥ colou≥ a≤ iε Flip.
  465.  
  466. VARYIN╟ CURSO╥ CONSTRAINTS║ MEMORYLES╙ FLI╨ AN─ FIR┼ FLIP
  467.  
  468.     Memoryles≤ Fli≡ i≤ identica∞ t∩ Fli≡ excep⌠ tha⌠ thσ curso≥ ma∙ movσ ì
  469. ont∩ thσ squarσ froφ whicΦ i⌠ jus⌠ came«  I⌠ i≤ calleΣ Memoryles≤ Fli≡ ì
  470. becausσ thσ curso≥ can'⌠ remembe≥ wherσ i⌠ ha≤ been.
  471.  
  472.     Firσ Fli≡ i≤ identica∞ t∩ Fli≡ excep⌠ tha⌠ thσ curso≥ ma∙ no⌠ movσ oε ì
  473. an∙ oµ thσ previou≤ ╞ square≤ (╞ i≤ ß natura∞ numbe≥ o≥ zero⌐ tha⌠ i⌠ ha≤ ì
  474. visited«  I⌠ i≤ calleΣ Firσ Fli≡ becausσ i⌠ i≤ a≤ iµ thσ curso≥ leave≤ ì
  475. behinΣ ß trai∞ oµ slowl∙ dyinτ firσ tha⌠ i⌠ canno⌠ ste≡ on«  Thσ zer∩ casσ ì
  476. oµ Firσ Fli≡ i≤ Memoryles≤ Flip.
  477.  
  478. PUR┼ FLIP
  479.  
  480.      Wheε analysi≤ oµ Fli≡ commenced¼ i⌠ wa≤ realizeΣ tha⌠ thσ systeφ oµ ì
  481. startinτ thσ gamσ witΦ thσ curso≥ iε thσ to≡ lef⌠ corne≥ witΦ i⌠ ablσ t∩ ì
  482. movσ dowε o≥ righ⌠ wa≤ inelegan⌠ a≤ i⌠ wa≤ thσ onl∙ timσ durinτ ß gamσ wheε ì
  483. thσ curso≥ coulΣ bσ iε ß corne≥ anΣ ablσ t∩ movσ iε morσ thaε onσ ì
  484. direction«  I⌠ wa≤ als∩ decideΣ tha⌠ thσ gamσ woulΣ bσ morσ interestinτ t∩ ì
  485. analysσ iµ onl∙ onσ colou≥ wa≤ thσ targe⌠ colour.
  486.  
  487.     Purσ Fli≡ i≤ identica∞ t∩ Fli≡ excep⌠ tha⌠ thσ curso≥ start≤ iε ß ì
  488. randoml∙ choseε squarσ witΦ ß randoφ history«  A≤ wel∞ a≤ this¼ therσ i≤ ìèonl∙ onσ solutioε statσ anΣ tha⌠ i≤ thσ wholσ boarΣ beinτ oµ thσ firs⌠ ì
  489. colour.
  490.  
  491.     Thu≤ Purσ Fli≡ i≤ ß combinatioε oµ Fastidiou≤ Fli≡ anΣ Firσ Flip(1).
  492.  
  493.  
  494. SUPE╥ FLIP
  495.  
  496.     Jus⌠ t∩ provσ tha⌠ al∞ thσ variation≤ caε bσ combineΣ withou⌠ ì
  497. difficulty¼ thei≥ ful∞ combinatioε calleΣ Supe≥ Fli≡ i≤ no≈ described.
  498.  
  499.     Therσ i≤ ß collectioε oµ node≤ Nπ wherσ π range≤ froφ ▒ t∩ T«  EacΦ ì
  500. nodσ i≤ connecteΣ viß ß unidirectiona∞ linδ t∩ thσ node≤ iε Rc¼ ß noε ì
  501. stric⌠ subse⌠ oµ thσ se⌠ oµ nodes«  Therσ exist≤ ╙ colour≤ H2..Hs«  A⌠ an∙ ì
  502. time¼ eacΦ nodσ iε thσ grapΦ i≤ coloureΣ onσ oµ thesσ colours«  Therσ arσ ╦ ì
  503. cursors«  EacΦ curso≥ ha≤ ß memor∙ lengtΦ ═ wherσ ═ i≤ zer∩ o≥ ß natura∞ ì
  504. number.
  505.  
  506.     A⌠ thσ star⌠ oµ thσ game¼ eacΦ nodσ i≤ coloureΣ randoml∙ froφ thσ se⌠ ì
  507. oµ colour≤ H1...Hs«  EacΦ curso≥ i≤ randoml∙ allocateΣ ß nodσ anΣ ß histor∙ ì
  508. oµ lengtΦ M.
  509.  
  510.     Durinτ eacΦ move¼ thσ playe≥ select≤ ß curso≥ anΣ move≤ i⌠ froφ thσ ì
  511. nodσ i⌠ i≤ oε t∩ aε accessiblσ node«  ┴ nodσ N│ i≤ accessiblσ t∩ nodσ N▒ iµ ì
  512. N│ i≤ ß membe≥ oµ R1«  Wheε ß curso≥ land≤ oε ß nodσ ¼ thσ node'≤ colou≥ i≤ ì
  513. changed«  Iµ thσ olΣ colou≥ i≤ Hu¼ thσ ne≈ colou≥ i≤ H1+(⌡ moΣ s).
  514.  
  515.     Thσ solutioε statσ i≤ tha⌠ iε whicΦ al∞ node≤ arσ oµ thσ colou≥ H1.
  516.  
  517.  
  518.                  ┴ ╬ ┴ ╠ ┘ ╙ ╔ ╙   ╧ ╞   ╞ ╠ ╔ P
  519.  
  520.  
  521.     Fli≡ i≤ ß gamσ tha⌠ i≤ highl∙ amenablσ t∩ mathematica∞ analysi≤  anΣ t∩ ì
  522. thi≤ end¼ thi≤ sectioε ha≤ beeε includeΣ containinτ fact≤ anΣ discoverie≤ ì
  523. abou⌠ Flip.
  524.  
  525.     Iµ yo⌡ wan⌠ t∩ bσ kep⌠ u≡ t∩ datσ witΦ an∙ morσ comprehensivσ analyse≤ ì
  526. made¼ writσ t∩ Grotniδ Software.
  527.  
  528.  
  529. CONTRIBUTORS
  530.  
  531.     Thσ followinτ notatioε i≤ useΣ t∩ represen⌠ contributor≤ t∩ thi≤ ì
  532. section« AH║ Andre≈ Hensel¼ RW║ Ros≤ Williams.
  533.  
  534.  
  535. TERMINOLOGY
  536.  
  537.     ¬ ┴ patternü refer≤ t∩ thσ boarΣ statσ no⌠ includinτ thσ curso≥ positioε ì
  538. anΣ orientation«  ┴ configurationü  refer≤ t∩ thσ boarΣ statσ includinτ thσ ì
  539. curso≥ positioε anΣ orientation« ¡-RW
  540.  
  541.  
  542. èSIMPL┼ FACTS
  543.  
  544. ¬ Fli≡ use≤ ß 4x┤ griΣ witΦ ß tota∞ oµ 4x4=1╢ squares«  A≤ eacΦ oµ thesσ ì
  545. square≤ caε bσ iε onσ oµ thσ tw∩ state≤ thσ tota∞ numbe≥ oµ differen⌠ ì
  546. pattern≤ possiblσ i≤ 216=65536« ¡-RW
  547.  
  548. ¬ Ou⌠ oµ al∞ oµ thσ pattern≤ possiblσ iε 4x┤ Flip¼ tw∩ configurations¼ onσ ì
  549. al∞ whitσ anΣ onσ al∞ blacδ arσ solutioε patterns«  Thu≤ therσ i≤ ß ▓ iε ì
  550. 6553╢ o≥ ▒ iε 3276╕ o≥ 0.000030╡ chancσ oµ winninτ thσ gamσ iε ░ moves!í ¡-ì
  551. RW
  552.  
  553. ¬ Purσ 3x│ Fli≡ ha≤ beeε solveΣ completel∙ witΦ thσ aiΣ oµ ß computer«  Thσ ì
  554. maximuφ numbe≥ oµ move≤ requireΣ t∩ g∩ froφ an∙ configuratioε oµ Purσ 3x│ ì
  555. Fli≡ t∩ an∙ othe≥ i≤ 24« ¡-AH
  556.  
  557. ¬ Aε upperbounΣ oε thσ maximuφ numbe≥ oµ move≤ requireΣ t∩ g∩ froφ an∙ ì
  558. configuratioε oµ Purσ Fli≡ t∩ an∙ othe≥ i≤ 47«  Thi≤ i≤ no⌠ ß leas⌠ ì
  559. upperbound« ¡-AH
  560.  
  561.  
  562. MUSINGS
  563.  
  564.    A╚ ha≤ pointeΣ ou⌠ onσ implicatioε oµ thσ wa∙ iε whicΦ thσ gamσ starts«  ì
  565. A⌠ present¼ a⌠ thσ star⌠ oµ eacΦ game¼ thσ curso≥ i≤ placeΣ iε thσ to≡ lef⌠ ì
  566. corne≥ oµ thσ griΣ anΣ initiall∙ i⌠ i≤ possiblσ t∩ movσ eithe≥ dowε o≥ ì
  567. right«  Thi≤ situatioε neve≥ arise≤ iε thσ coursσ oµ ß gamσ wherσ wheneve≥ ì
  568. thσ playe≥ i≤ iε ß corner¼ therσ i≤ onl∙ onσ choice«  T∩ alleviatσ this¼ ì
  569. Purσ Fli≡ ha≤ beeε createΣ incorporatinτ thi≤ anΣ anothe≥ modification«  ì
  570. Seσ sectioε 6║ Variation≤ oε Flip«  Futurσ version≤ oµ thσ Fli≡ program¼ ì
  571. wil∞ probabl∙ bσ Purσ Flip« ¡-RW
  572.  
  573. ¬  ┴ deepe≥ reasoε arise≤ fo≥ ß changeove≥ t∩ Purσ Flip«  Thσ gamσ woulΣ bσ ì
  574. morσ elegan⌠ iµ thσ gamσ starteΣ iε ß statσ tha⌠ coulΣ bes⌠ bσ describeΣ a≤ ì
  575. ß "stead∙ state"«  Thσ neares⌠ tha⌠ caε bσ achieveΣ t∩ thi≤ i≤ ß randoφ ì
  576. configuratioε witΦ ß randoφ curso≥ positioε anΣ randoφ directiona∞ ì
  577. constraints«   A╚ say≤ tha⌠ thσ initia∞ configuratioε oµ thσ gamσ woulΣ bσ ì
  578. tha⌠ oµ ß gamσ pu⌠ dowε fo≥ ß momen⌠ b∙ ß Martiaε wh∩ ha≤ beeε randoml∙ ì
  579. playinτ witΦ thσ puzzle«¡-RW
  580.  
  581. ¬  ┴ se⌠ oµ move≤ iε Fli≡ arσ likσ ß foldeΣ stri≡ oµ pape≥ tha⌠ caε bσ ì
  582. placeΣ ove≥ thσ board«  Thσ overal∞ resul⌠ oµ thσ se⌠ oµ move≤ caε bσ ì
  583. determineΣ b∙ thσ odd/evennes≤ oµ thσ numbe≥ oµ layer≤ oµ pape≥ ove≥ eacΦ ì
  584. square« ¡-AH
  585.  
  586.  
  587. PROO╞ O╞ SOLUBILIT┘ O╞ FLIP
  588.  
  589.     Thi≤ prooµ demonstrate≤ tha⌠ i⌠ i≤ possiblσ t∩ g∩ froφ an∙ patterε oµ ì
  590. Fli≡ t∩ an∙ othe≥ anΣ place≤ aε upperbounΣ oε thσ numbe≥ oµ move≤ requireΣ ì
  591. t∩ d∩ so.
  592.  
  593.     Thσ prooµ i≤ baseΣ upoε provinτ tha⌠ regardles≤ oµ initia∞ o≥ fina∞ ì
  594. curso≥ position¼  ß finitσ sequencσ oµ move≤ (t∩ bσ collectivel∙ referreΣ ì
  595. t∩ a≤ ß move⌐ exist≤ tha⌠ wil∞ fli≡ an∙ giveε squarσ anΣ tha⌠ squarσ only«  ì
  596. Iµ thσ existencσ oµ sucΦ ß movσ fo≥ eacΦ squarσ oµ an∙ configuratioε caε bσ ìèproved¼ theε i⌠ follow≤ tha⌠ ß sourcσ patterε ma∙ bσ changeΣ t∩ ß targe⌠ ì
  597. configuratioε usinτ ß move«  A≤ therσ i≤ ß finitσ numbe≥ oµ squares¼ thσ ì
  598. upperbounΣ oµ thσ numbe≥ oµ move≤ requireΣ i≤ finite.
  599.  
  600.     Herσ i≤ thσ prooµ tha⌠ ß movσ exist≤ fo≥ an∙ square«  Takσ thσ targe⌠ ì
  601. squarσ anΣ fi⌠ onσ oµ thσ followinτ template≤ ont∩ thσ boarΣ s∩ tha⌠ thσ ì
  602. squarσ oε thσ templatσ markeΣ ╘ (fo≥ target⌐ i≤ oε to≡ oµ thσ targe⌠ squarσ ì
  603. anΣ s∩ tha⌠ al∞ oµ thσ templatσ i≤ oε thσ board«  Tha⌠ thi≤ i≤ alway≤ ì
  604. possiblσ i≤ easil∙ showε througΦ ß casσ analysi≤ oµ thσ variou≤ type≤ oµ ì
  605. boarΣ square║ corner¼ sidσ anΣ centre.
  606.  
  607. ½¡¡¡¡¡¡¡¡¡¡¡-½                  ½¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡-+
  608. ║     ║      ║                  ║      ║     ║     :
  609. ║     ║      ║                  ║      ║     ║     :
  610. ║¡¡¡¡-½¡¡¡¡¡-║                  ║¡¡¡¡¡-½¡¡¡¡-½¡¡¡¡-+
  611. ║     ║      ║                  ║      ║     ║     :
  612. ║     ║      ║                  ║      ║     ║     :
  613. ║¡¡¡¡-½¡¡¡¡¡-½                  ║¡¡¡¡¡-½¡¡¡¡-║¡¡¡¡-:
  614. ║     ║ ⁿ ¡ ⁿ ¡ ⁿ ¡ ⁿ ¡ |ⁿ      ║      ║ |ⁿ ¡ ¡ ⁿ ¡ ⁿ ¡ ⁿ ¡ ¡ |
  615. ║     ║                         ║      :
  616. ½¡¡¡¡-½                         ½¡¡¡¡¡-+
  617. Fig« A«                         Fig« B.
  618.  
  619. Move≤ showε fo≥ Fiτ ┴ arσ a≤ follows║ U¼ R¼ U¼ L¼ D¼ R¼ U¼ L¼ D¼ D.
  620.  
  621. Move≤ showε fo≥ Fiτ ┬ are║ U¼ U¼ R¼ R¼ D¼ L¼ U¼ R¼ D¼ L¼ L¼ D.
  622.  
  623.  
  624.     Thσ sequencσ oµ move≤ oµ thσ movσ i≤ a≤ follows║-
  625.  
  626. 1«  Movσ thσ curso≥ t∩ thσ squarσ markeΣ oε thσ templatσ a≤ ╙ (fo≥ start)«  ì
  627. Thσ curso≥ mus⌠ bσ orienteΣ s∩ tha⌠ i⌠ i≤ ablσ t∩ movσ iε thσ directioε ì
  628. froφ ╙ t∩ T.
  629.  
  630. 2«  Appl∙ thσ sequencσ oµ move≤ listeΣ unde≥ thσ choseε template.
  631.  
  632. 3«  Retracσ thσ patΦ followeΣ iε 1¼ thu≤ reversinτ thσ damage.
  633.  
  634.  
  635.     Thi≤ flip≤ thσ squarσ markeΣ ╘ withou⌠ flippinτ an∙ othe≥ squares«  Thσ ì
  636. fac⌠ tha⌠ thσ directioε oµ thσ curso≥ i≤ changeΣ i≤ immateria∞ a≤ thi≤ wa≤ ì
  637. no⌠ ß preconditioε oµ applyinτ thσ move¼ anΣ move≤ arσ al∞ wσ appl∙ t∩ ì
  638. solvσ thσ puzzle.
  639.  
  640.     Becausσ i⌠ i≤ possiblσ t∩ g∩ froφ an∙ patterε t∩ an∙ othe≥ viß ß ì
  641. sequencσ oµ moves¼ i⌠ mus⌠ bσ possiblσ t∩ g∩ froφ an∙ patterε t∩ ß solutioε ì
  642. pattern«  Hencσ ever∙ configuratioε oµ Fli≡ i≤ solvable«¡-AH
  643.  
  644.  
  645. PROBLEM╙ O╞ INTEREST
  646.  
  647. ¬ EacΦ Purσ Fli≡ boarΣ configuratioε ha≤ ß numbe≥ tha⌠ i≤ thσ minimuφ ì
  648. numbe≥ oµ move≤ tha⌠ arσ requireΣ t∩ solvσ thσ configuration«  Wha⌠ i≤ thσ ì
  649. maximuφ oµ thσ se⌠ oµ minimums┐  Fo≥ 3x│ Purσ Fli≡ i⌠ i≤ 24«¡-RW
  650. 謠Thσ solutioε t∩ Fli≡ embodieΣ iε thσ prooµ oµ solvabilit∙ abovσ supplie≤ ì
  651. ß soliΣ bu⌠ ver∙ higΦ upperbounΣ oε thσ numbe≥ oµ move≤ requireΣ t∩ solvσ ì
  652. thσ game«  I⌠ woulΣ bσ interestinτ t∩ finΣ ß morσ efficien⌠ method«  Onσ ì
  653. ha≤ beeε founΣ witΦ aε upperbounΣ oµ 47«  Caε yo⌡ d∩ better?
  654.  
  655.  
  656.         ┴ ╨ ╨ ┼ ╬ ─ ╔ ╪   A║   ╠ ╧ ┴ ─ ╔ ╬ ╟   ╞ ╠ ╔ P
  657.  
  658.     Thi≤ sectioε describe≤ ho≈ t∩ loaΣ anΣ ruε Fli≡ froφ thσ variou≤ ì
  659. medium≤ upoε whicΦ i⌠ i≤ sold«  Variation≤ iε thσ precisσ wa∙ iε whicΦ thσ ì
  660. prograφ i≤ recordeΣ ma∙ occu≥ froφ timσ t∩ time«  An∙ majo≥ change≤ wil∞ bσ ì
  661. documenteΣ separatel∙ anΣ thosσ instruction≤ wil∞ supplemen⌠ anΣ supersedσ ì
  662. thesσ ones.
  663.  
  664. CASSETT┼ TAPES
  665.  
  666.     Thσ Fli≡ cassettσ ha≤ threσ 120░ bauΣ copie≤ oµ thσ prograφ recordeΣ oε ì
  667. onσ side¼ anΣ onσ 30░ bauΣ cop∙ recordeΣ oε sidσ two«  Fli≡ take≤ abou⌠ onσ ì
  668. minutσ t∩ loaΣ a⌠ 120░ bauΣ anΣ abou⌠ threσ minute≤ t∩ loaΣ a⌠ 30░ baud«  ì
  669. Upoε purchasσ thσ cassettσ woulΣ bσ rewounΣ t∩ sidσ one.
  670.  
  671.     T∩ loaΣ anΣ ruε Flip¼ pu⌠ thσ cassettσ iε you≥ cassettσ uni⌠ anΣ froφ ì
  672. BASI├ typσ LOA─ anΣ hi⌠ thσ RETUR╬ key«  Pres≤ PLA┘ oε thσ cassettσ uni⌠ ì
  673. anΣ thσ prograφ wil∞ loaΣ anΣ bσ ruε automatically.
  674.  
  675.  
  676. 5.25ó FLOPP┘ DISK╙ AN─ 3.5ó DISKS
  677.  
  678.     Thσ terφ distributioε disδ useΣ iε thσ followinτ refer≤ t∩ thσ disδ ì
  679. tha⌠ yo⌡ havσ jus⌠ purchased.
  680.  
  681.     Fli≡ oε disδ i≤ solΣ oε MicroBeσ standarΣ forma⌠ 5.25ó disk≤ anΣ oε thσ ì
  682. ne≈ compute≥-iε-ß-booδ 3.5ó disks.
  683.  
  684.     Thσ distributioε disδ i≤ formatteΣ anΣ ha≤ writteε upoε i⌠ ß singlσ ì
  685. .CO═ file«  Thσ distributioε disδ doe≤ no⌠ havσ thσ operatinτ systeφ (CP/M⌐ ì
  686. oε i⌠ s∩ d∩ no⌠ attemp⌠ t∩ boo⌠ you≥ disδ systeφ froφ it.
  687.  
  688.     Thσ .CO═ filσ oε thσ distributioε disδ consist≤ firstl∙ oµ seventeeε ì
  689. bytσ loade≥ anΣ theε thσ prograφ itselµ whicΦ i≤ identica∞ t∩ thσ tapσ ì
  690. version.
  691.  
  692.     ┴ loade≥ i≤ useΣ s∩ tha⌠ exactl∙ thσ samσ versioε oµ ß prograφ caε bσ ì
  693. useΣ fo≥ botΦ disδ anΣ tape«  Thi≤ mean≤ tha⌠ therσ i≤ onl∙ onσ curren⌠ ì
  694. versioε oµ Fli≡ prograφ regardles≤ oµ thσ mediuφ upoε whicΦ i⌠ i≤ sold.
  695.  
  696.     T∩ ruε thσ program¼ yo⌡ mus⌠ boo⌠ you≥ disδ systeφ anΣ executσ thσ ì
  697. Flip.CO═ filσ oε thσ distributioε disk«  Contro∞ wil∞ returε t∩ CP/═ afte≥ ì
  698. execution.
  699.  
  700. 1« Bootinτ thσ Disδ System
  701. Wσ assumσ tha⌠ yo⌡ kno≈ ho≈ t∩ boo⌠ you≥ disδ systeφ anΣ makσ thσ ì
  702. distributioε disδ thσ defaul⌠ disk«  Iµ yo⌡ don't¼ refe≥ t∩ you≥ MicroBeσ ì
  703. Disδ Systeφ Manual«  D∩ no⌠ tr∙ bootinτ ofµ thσ distributioε disδ a≤ i⌠ ì
  704. doe≤ no⌠ havσ ß cop∙ oµ thσ operatinτ systeφ oε it.
  705. è2« Executinτ thσ FLIP.CO═ File
  706.  
  707. ┴ director∙ oµ thσ distributioε disδ wil∞ revea∞ ß singlσ Flip.CO═ file«  ì
  708. Thσ .CO═ filσ i≤ thσ prograφ anΣ ma∙ bσ executeΣ b∙ typinτ it≤ namσ FLI╨ ì
  709. withou⌠ thσ filσ extension«  Thus¼ iε orde≥ t∩ ruε FLIP.COM¼ yo⌡ neeΣ onl∙ ì
  710. givσ thσ commanΣ FLI╨ wheε thσ CP/═ promp⌠ (eg║ A>⌐ come≤ up.
  711.  
  712. Returninτ t∩ CP/M
  713.  
  714. Wheε yo⌡ exi⌠ thσ program¼ contro∞ wil∞ returε t∩ CP/═ viß ß warφ boot«  I⌠ ì
  715. i≤ thereforσ importan⌠ t∩ ensurσ tha⌠ therσ i≤ ß disδ witΦ thσ CP/═ ì
  716. operatinτ systeφ oε i⌠ iε thσ boo⌠ drivσ wheε yo⌡ exi⌠ thσ program«  Al∞ ì
  717. carσ ha≤ beeε takeε t∩ ensurσ tha⌠ thσ prograφ doe≤ no⌠ upse⌠ CP/═ bu⌠ n∩ ì
  718. responsibilit∙ i≤ takeε fo≥ thσ consequence≤ oµ undefineΣ systeφ state≤ ì
  719. upoε returninτ t∩ CP/M.
  720.  
  721.  
  722. EPROMS
  723.  
  724.     Fli≡ iε chi≡ forφ i≤ solΣ a≤ ß singlσ 276┤ EPRO═ tha⌠ i≤ suitablσ fo≥ ì
  725. instal∞atioε iε serie≤ II╔ RO═ baseΣ MicroBees.
  726.  
  727.     T∩ usσ thσ chip¼ yo⌡ wil∞ firs⌠ havσ t∩ instal∞ i⌠ iε you≥ MicroBee«  ┴ ì
  728. ful∞ descriptioε oµ ho≈ t∩ d∩ thi≤ appear≤ iε ß sectioε titleΣ Addinτ Morσ ì
  729. Interna∞ RO═ Softwareü iε thσ bookle⌠ Serie≤ II╔ Microbeσ User≤ Manualü tha⌠ ì
  730. i≤ issueΣ witΦ eacΦ Serie≤ II╔ MicroBee«  I⌠ i≤ pagσ 5│ iε m∙ copy«  Thσ ì
  731. followinτ ma∙ als∩ bσ useΣ a≤ ß guide.
  732.  
  733.     Firs⌠ oµ all¼ thσ to≡ cove≥ oµ thσ MicroBeσ mus⌠ bσ removeΣ t∩ exposσ ì
  734. thσ to≡ RO═ anΣ RA═ board«  T∩ d∩ this¼ turε thσ MicroBeσ upsidσ down«  Yo⌡ ì
  735. wil∞ theε bσ faceΣ witΦ si° screws«  Unscre≈ thσ tw∩ oε thσ lef⌠ anΣ righ⌠ ì
  736. hanΣ sidσ oµ thσ bacδ oµ thσ MicroBee«  Pu⌠ thσ screw≤ somewherσ safe¼ theε ì
  737. turε thσ MicroBeσ ove≥ agaiε anΣ gentl∙ lif⌠ thσ to≡ ofµ thσ raiseΣ ì
  738. section.
  739.  
  740.     Thi≤ wil∞ exposσ aε arra∙ oµ biτ fa⌠ chip≤ anΣ somσ socket≤ oµ simila≥ ì
  741. size«  Thσ sockets¼ somσ oµ whicΦ ma∙ alread∙ bσ filleΣ arσ fo≥ EPROMS«  ì
  742. EacΦ socke⌠ ha≤ ß correspondinτ number«  Herσ i≤ ß diagraφ oµ wha⌠ yo⌡ ì
  743. shoulΣ see:
  744.  
  745.                     BAC╦ O╞ MICROBEE
  746.  
  747. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  748. :°     ║  :°     ║  :°     ║  :°     :
  749. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  750.  
  751. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  752. :°     ║  :°     ║  :°     ║  :°     ║  ║ SOC┤ ║  ║ SOC╡ :
  753. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  754.  
  755. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  756. :°     ║  :°     ║  :°     ║  :°     ║  ║ SOC│ :
  757. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  758.  
  759. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+è:°     ║  :°     ║  :°     ║  :°     ║  ║ SOC▓ :
  760. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  761.  
  762. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  763. :°     ║  :°     ║  :°     ║  :°     ║  ║ SOC▒ :
  764. ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-½  ½¡¡¡¡¡-+
  765.                   FRON╘ O╞ MICROBEE
  766.  
  767.  
  768.     Choosσ thσ socke⌠ witΦ thσ lowes⌠ numbe≥ froφ thσ se⌠ oµ empt∙ socket≤ ì
  769. theε inser⌠ thσ chi≡ a≤ follows«  I⌠ i≤ ß gooΣ ideß no⌠ t∩ toucΦ thσ pin≤ ì
  770. oµ thσ chi≡ durinτ thi≤ process.
  771.  
  772.     Firs⌠ oµ al∞ identif∙ thσ notcΦ oε onσ oµ thσ shor⌠ side≤ oµ thσ EPROM«  ì
  773. Wheε yo⌡ inser⌠ thσ chip¼ thi≤ notcΦ shoulΣ facσ iε thσ samσ directioε a≤ ì
  774. thσ notche≤ oµ thσ othe≥ chip≤ (seσ diagram)«  GraΓ thσ chi≡ a⌠ eithe≥ enΣ ì
  775. anΣ pul∞ i⌠ ou⌠ oµ it≤ foaφ holder«  Tr∙ t∩ inser⌠ i⌠ int∩ thσ choseε ì
  776. socke⌠ rememberinτ t∩ ge⌠ thσ notcΦ direction«  Iµ yo⌡ finΣ tha⌠ thi≤ i≤ ì
  777. difficul⌠ becausσ thσ leg≤ oµ thσ chi≡ arσ to∩ spreaΣ ou⌠ theε i⌠ ma∙ bσ ì
  778. helpfu∞ t∩ benΣ thσ pin≤ oε onσ sidσ b∙ pushinτ thσ chi≡ a⌠ aε anglσ ont∩ ß ì
  779. fla⌠ surfacσ beforσ inserting.
  780.  
  781.     Thσ EPRO═ contain≤ ß twent∙ bytσ loade≥ anΣ theε thσ prograφ itselµ ì
  782. whicΦ i≤ identica∞ t∩ thσ tapσ version.
  783.  
  784.     T∩ ruε thσ prograφ givσ thσ PAk° commanΣ wherσ ° i≤ thσ numbe≥ oµ thσ ì
  785. EPRO═ socke⌠ int∩ whicΦ yo⌡ inserteΣ thσ chip«  Oncσ yo⌡ havσ issueΣ thσ ì
  786. PA╦ command¼ thσ prograφ shoulΣ ruε immediately«  Iµ i⌠ doe≤ no⌠ theε ì
  787. somethinτ i≤ wrong«  Checδ tha⌠ thσ chi≡ i≤ inserteΣ properl∙ anΣ tha⌠ yo⌡ ì
  788. havσ giveε thσ PA╦ commanΣ correctly.
  789.  
  790.     Wheε yo⌡ exi⌠ Flip¼ thσ compute≥ wil∞ rese⌠ s∩ makσ surσ tha⌠ yo⌡ d∩ ì
  791. no⌠ havσ an∙ preciou≤ informatioε iε memor∙ wheε yo⌡ givσ thσ PA╦ command.
  792.  
  793.  
  794.  
  795.  
  796.  
  797.  
  798.  
  799.  
  800.  
  801.  
  802.  
  803.  
  804.  
  805.  
  806.  
  807.  
  808.  
  809.  
  810.  
  811.  
  812.  
  813. è┴ ╨ ╨ ┼ ╬ ─ ╔ ╪   B║  ╦ ┼ ┘ ═ ┴ ╨   ╞ ╧ ╥   ╞ ╠ ╔ P
  814.  
  815. RU╬ MODE
  816.  
  817.     Herσ i≤ ß ma≡ oµ al∞ thσ key≤ t∩ whicΦ Fli≡ wil∞ responΣ durinτ ß game«  ì
  818. A⌠ al∞ othe≥ times¼ Fli≡ indicateΣ iε it≤ promp⌠ wha⌠ actioε i≤ requireΣ ì
  819. anΣ s∩ thosσ othe≥ mode≤ havσ no⌠ beeε documenteΣ here.
  820.  
  821.      Abort
  822.      Current
  823.      Game
  824.       »               U≡     SounΣ   Vie≈ Instruction≤      Up
  825. ½¡¡¡¡¡-½              »      ▄                »              /
  826. ║ ES├  ║             »        ▄              »              »  Right
  827. ½¡¡¡¡¡-½        ½¡¡¡¡¡-½        ▄       ½¡¡¡¡¡-½        ½¡¡¡¡¡-½ |
  828.                 ║   ╫  ║         ▄      ║   ╔  ║        ║   █  ║ |
  829.              ½¡¡¡¡-½¡¡¡¡¡-½ ½¡¡¡¡¡-½ ½¡¡¡¡¡-½¡-½     ½¡¡¡¡¡-½¡¡¡¡¡-+
  830.              ║  ┴  ║   ╙  ║ ║   ╟  ║ ║  ╩   ║        ║   ╗  ║   └  :
  831.              ½¡¡¡¡-½¡¡¡¡¡-½ ½¡¡¡¡¡-½ ½¡¡¡¡¡-½        ½¡¡¡¡¡-½¡¡¡¡¡-+
  832.                /║  ┌   :▄                »            » ║   »  :
  833.               » ½¡¡¡¡¡-½ ▄              »            »  ½¡¡¡¡¡-+
  834.           Lef⌠          Righ⌠       Joysticδ       Lef⌠       \
  835.                                      On/Ofµ                  Down
  836.  
  837.  
  838.  
  839. ┴ ╨ ╨ ┼ ╬ ─ ╔ ╪   C║ ╘ ┼ ├ ╚ ╬ ╔ ├ ┴ ╠   ╔ ╬ ╞ ╧ ╥ ═ ┴ ╘ ╔ ╧ N
  840.  
  841.     Herσ i≤ ß shor⌠ lis⌠ oµ importan⌠ addresse≤ iε thσ Fli≡ prograφ tha⌠ ì
  842. ma∙ bσ usefu∞ iµ yo⌡ arσ havinτ troublσ runninτ thσ program«  I⌠ shoulΣ ì
  843. als∩ bσ usefu∞ iµ yo⌡ wan⌠ t∩ takσ ß backu≡ cop∙ o≥ savσ i⌠ oε ß differen⌠ ì
  844. medium.
  845.  
  846.         1000║  Star⌠ Address.
  847.           1000║  G∩ Address.
  848.           1009║  Star⌠ oµ Prσ-I├ 3░ b∙ 6┤ vide∩-registe≥ values.
  849.           1019║  Star⌠ oµ     I├ 3░ b∙ 6┤ vide∩-registe≥ values.
  850.           22D8║  EnΣ addres≤ oµ Fli≡ program.
  851.  
  852.  
  853.     Fli≡ doe≤ no⌠ cal∞ an∙ externa∞ routine≤ (eg« Monito≥ o≥ BASIC).
  854.  
  855.     Fli≡ program≤ thσ vide∩ register≤ t∩ makσ thσ screeε 3░ ° 6┤ ì
  856. characters«  Despitσ this¼ Fli≡ ma∙ bσ ruε oε ß variet∙ oµ MicroBee≤ a≤ i⌠ ì
  857. adapt≤ itselµ fo≥ each«  However¼ therσ ha≤ beeε somσ difficult∙ witΦ thi≤ ì
  858. iε thσ past«  Iµ you≥ cop∙ load≤ ofµ thσ tapσ bu⌠ doe≤ no⌠ ruε properl∙ ì
  859. (esp« thσ screeε lookinτ likσ ß sicδ oscilloscope)¼ theε i⌠ ma∙ bσ ß ì
  860. probleφ witΦ thσ vide∩ programming«  Iµ thi≤ happens¼ writσ t∩ Grotniδ ì
  861. Softwarσ anΣ the∙ wil∞ bσ happ∙ eithe≥ t∩ fi° thσ probleφ o≥ arrangσ aε ì
  862. adjustment.
  863.  
  864.     Fli≡ i≤ locateΣ a⌠ 1000╚ t∩ ge⌠ i⌠ awa∙ froφ al∞ thσ critica∞ memor∙ ì
  865. (eg« interrup⌠ vector≤ anΣ thσ monitor'≤ worδ area⌐ tha⌠ thσ MicroBeσ ha≤ ì
  866. lowe≥ dowε iε memory.
  867. èVERSIO╬ NUMBERS
  868.  
  869.     Fli≡ ha≤ ß versioε numbe≥ t∩ aiΣ iε thσ reportinτ oµ problems«  Versioε ì
  870. number≤ arσ representeΣ a≤ tw∩ digit≤ separateΣ b∙ ß dot«  Thσ firs⌠ digi⌠ ì
  871. i≤ thσ rewritσ coun⌠ anΣ thσ seconΣ i≤ thσ modificatioε count«  Thσ versioε ì
  872. numbe≥ i≤ displayeΣ a⌠ thσ to≡ oµ thσ screeε instructions.
  873.  
  874.     Thesσ instruction≤ werσ writteε wheε versioε 1.░ oµ Fli≡ wa≤ current«  ì
  875. iµ yo⌡ havσ ß late≥ versioε therσ wil∞ probabl∙ bσ loosσ sheet≤ ì
  876. accompanyinτ thesσ instructions«  Thσ informatioε oε sucΦ sheet≤ ì
  877. supplement≤ anΣ supersede≤ thesσ instructions.
  878.  
  879.  
  880.  
  881. ┴ ╨ ╨ ┼ ╬ ─ ╔ ╪   D║  ├ ╧ ╨ ┘ ╥ ╔ ╟ ╚ ╘   ╬ ╧ ╘ ╔ ├ E
  882.  
  883.     AlthougΦ createΣ year≤ before¼ thσ Fli≡ gamσ wa≤ firs⌠ explicitl∙ ì
  884. copyrighteΣ iε 198▓ wheε i⌠ wa≤ releaseΣ fo≥ thσ Sorcere≥ computer«  Thσ ì
  885. gamσ iε al∞ it≤ form≤ remain≤ copyright«  Anyonσ wishinτ t∩ rewritσ o≥ ì
  886. distributσ thi≤ gamσ iε an∙ forφ mus⌠ obtaiε prio≥ permissioε iε writinτ t∩ ì
  887. Ros≤ Williams« 
  888.  
  889.     Thi≤ softwarσ anΣ thσ accompanyinτ instruction≤ arσ copyrigh⌠ (c⌐ 198╡ ì
  890. b∙ Ros≤ Williams.
  891.  
  892.     Customer≤ arσ remindeΣ oµ thσ law≤ relatinτ t∩ copyrigh⌠ whicΦ prohibi⌠ ì
  893. unauthoriseΣ copyinτ oµ compute≥ programs«  However¼ customer≤ ma∙ makσ ì
  894. bacδ-u≡ copie≤ fo≥ thei≥ privatσ usσ only.
  895.  
  896.  
  897.  
  898. ┴ ╨ ╨ ┼ ╬ ─ ╔ ╪   E║  ┴ ├ ╦ ╬ ╧ ╫ ╠ ┼ ─ ╟ ┼ ═ ┼ ╬ ╘ S
  899.  
  900.     Thσ origina∞ Flip¼ thσ ne≈ MicroBeσ versioε anΣ thesσ instruction≤ werσ ì
  901. al∞ writteε b∙ Ros≤ Williams«  Thσ "Flipwalkeró illustration≤ werσ ì
  902. extracteΣ froφ ß drawinτ b∙ R« Tomlaiε anΣ subsequentl∙ modifieΣ b∙ Ros≤ ì
  903. Williams«  Piratσ drawinτ b∙ R« Tomlain«  Al∞ othe≥ artworδ b∙ Ros≤ ì
  904. Williams«  Thank≤ t∩ Andre≈ Hense∞ fo≥ hi≤ contributioε t∩ thσ analysi≤ oµ ì
  905. thσ game.
  906.  
  907.  
  908.                 Kee≡ you≥ Fli≡ boarΣ beautiful.
  909.        Pleasσ disposσ oµ thσ blacδ square≤ thoughtfully!
  910.