Some of you may have heard of the recent growing trend of Digitless Outrageously Orange Fluorescent Upside-down Sudoku. In case you haven't heard of it, its description is exactly what it sounds like.
Digitless Outrageously Orange Fluorescent Upside-down Sudoku is played extremely similarly to the normal sudoku that you all may know about. It has some subtle slight differences to normal sudokus that are best left unexplained since not many people know how to deal with them at the moment. However, besides this, Digitless Outrageously Orange Fluorescent Upside-down Sudoku is vastly growing in popularity after a recent survey has indicated significant health benefits of doing it in place of normal sudoku.
Digitless Outrageously Orange Fluorescent Upside-down Sudoku has for one thing been discovered as a previously unknown cure for the common cold; not just in our familiar Homo sapiens, but in several other species too, notably blobfishes, robots, Saturnian aliens, that random guy with horrible voice in the film Up In The Air, and all sorts of odd brown leather suede shoes. It works in the same way as hand moisturising cream; when applied to the hands (and other body parts as appropriate) twice daily it ensures instant relief from the common cold for about twelve hours and eventually recovery altogether after five weeks.
Digitless Outrageously Orange Fluorescent Upside-down Sudoku also has significant mental health benefits too: it has been shown that even thrice weekly usage for ten years can improve IQ by up to fifteen points, which is one whole standard deviation on the globally regarded IQ scale (a normal distribution with mean one hundred and std dev fifteen). It has also been used in psychiatric wards to treat mentally unstable patients by holding them hostage and demanding several hundred pounds of ransom money, which somehow makes them sane again; the exact mechanism by which this happens is unclear.
Like ordinary sudoku, Digitless Outrageously Orange Fluorescent Upside-down Sudoku is completely free to play and is available in all parts of the world; all that is needed is a computer with slightly better encoding than the simple eight-bit character coding that comes with default on ancient computers; anything of Windows XP or higher may handle this efficiently, but encoding settings may need to be changed. However this is usually unnecessary.
Below is an example of the often prized Digitless Outrageously Orange Fluorescent Upside-down Sudoku (often abbreviated DOOFUS) which I believe many of you may recognise in some form or another. The complete solution path is underneath.
Ë™puÇ oʇ sÇlƃuıs ˙ʇɥƃıÇ-ʎʇuÇÊʇ
Ë™ÇÇɹɥʇ=/=ÇʌıɟuɯnloÉ”oÊʇÊoɹ <= ÇʌıɟʞɔolqÇÇɹɥʇ ɹnoÉŸÊoɹÇʌıɟ oÊʇÊoɹÇʌıɟ :Çuo-Çq-uÉɥʇ-ÇÇs-ɹÇɥʇÉɹ-p,ı-Êou-ʇɥƃıɹ-sıɥʇ-noÊŽ-llÇʇ-uÉÉ”-ı-ʇnq-Çuo-ÇÇs-ɹÇÊŒÇu-ı-ÇdoÉ¥-ı-ÊoÉ”-Çldɹnd-É-ÊÉs-ɹÇÊŒÇu-ı Ë™uÇÊŒÇs-ʎʇuÇÊʇ
Ë™Çʌıɟ=uÇÊŒÇsuɯnloÉ”ÇuıuÊoɹ Ë™xıs-ʎʇuÇÊʇ
Ë™Çʌıɟ=/=ÇʌıɟuɯnloÉ”ÇuıuÊoɹ <= ÇʌıɟuɯnloÉ”oÊʇʞɔolqÇʌıɟ ƃuıʇuıod Ë™Çʌıɟ-ʎʇuÇÊʇ
Ë™Çʌıɟ=/=ɹnoÉŸuɯnloÉ”oÊʇÊoɹ <= ÇʌıɟʞɔolqÇʌıɟ xısuɯnloÉ”ÇÇɹɥʇ oÊʇʞɔolquÇÊŒÇs :ƃuÄ±Ê pıɹqÊŽÉ¥ ˙ɹnoÉŸ-ʎʇuÇÊʇ
Ë™Çʌıɟ=/=xısuɯnloÉ”ÇʌıɟÊoɹ <= ÇʌıɟÊoɹuÇÊŒÇsÇuo ɹıÉd uÇppıɥ Ë™ÇÇɹɥʇ-ʎʇuÇÊʇ
Ë™Çuo=/=ɹnoÉŸuɯnloÉ”uÇÊŒÇsÊoɹɹnoÉŸÇÇɹɥʇuɯnloÉ”ÇʌıɟÊoɹ <= ÇuıuxısoÊʇuɯnloÉ”Çuo É¥sıɟpɹoÊs Ë™oÊʇ-ʎʇuÇÊʇ
˙ʇɥƃıÇoÊʇ=/=oÊʇuɯnloɔɹnoÉŸÊoɹ <= ɹnoÉŸÊoɹʇɥƃıÇoÊʇ ɹıÉd pÇÊžÉu Ë™Çuo-ʎʇuÇÊʇ
Ë™Çuıu=ɹnoÉŸuɯnloÉ”ÇʌıɟÊoɹ ˙ʎʇuÇÊʇ
Ë™Çuıu=/=ɹnoÉŸuɯnloÉ”ÇʌıɟÊoɹ <= ʇɥƃıÇuɯnloÉ”Çuıu ÇʌıɟuɯnloÉ”Çuıu É¥sıɟ ʇoqɹnʇ Ë™uÇÇʇÇuıu
Ë™uÇÊŒÇs=/=ʇɥƃıÇuɯnloÉ”ÇʌıɟÊoɹ <= ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÇÇɹɥʇ ɹıÉd pÇÊžÉu Ë™uÇÇʇɥƃıÇ
˙ɟlÇsɹnoÊŽ ʇı op Ë™sÇlƃuıs É¥Ê‡Ä±Ê ÇÊŒlos sɹnoÉŸ Çɥʇ llÉ Ë™uÇÇʇuÇÊŒÇs
Ë™uÇÊŒÇsÇÇɹɥʇ=/=ÇuouɯnloÉ”oÊʇÊoɹ <= uÇÊŒÇsʞɔolquÇÊŒÇs uÇÊŒÇsʞɔolqÇÇɹɥʇ uÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹÇuouɯnloÉ”ÇÇɹɥʇÊoɹuÇÊŒÇsÇÇɹɥʇ ƃuıÊ-Ê Çlqnop Ë™uÇÇʇxıs
˙ʇɥƃıÇ=/=ÇuıuuɯnloÉ”ÇʌıɟɹnoÉŸÊoɹ <= ÇuıuuɯnloÉ”ÇuıuʞɔolqÊ‡É¥ÆƒÄ±Ç Æƒuıʇuıod Ë™uÇÇʇɟıɟ
˙ʇɥƃıÇuÇÊŒÇsÇÇɹɥʇ=/=ʇɥƃıÇuÇÊŒÇsuɯnloÉ”ÇuıuÊoɹuÇÊŒÇsuɯnloÉ”uÇÊŒÇsÊoɹ <= ÇuıuʞɔolqʇɥƃıÇuÇÊŒÇsÇÇɹɥʇ ʇÇldıɹʇ pÇÊžÉu Ë™uÇÇʇɹnoÉŸ
˙ɟlÇsɹnoÊŽ ʇı op Ë™sÇlƃuıs É¥Ê‡Ä±Ê ÇÊŒlos sÇxıs Çɥʇ llÉ Ë™uÇÇʇɹıɥʇ
˙ɹnoÉŸ=xısuɯnloÉ”ÇuıuÊoɹ Ë™ÇÊŒlÇÊʇ
(oÊʇ ʞɔolq uı Ê‡É¥ÆƒÄ±Ç É¹oÉŸ ÇÉ”Éld ou) xıs=/=ÇuıuuɯnloɔʇɥƃıÇÊoɹ <= ʇɥƃıÇ-ÇʌıɟuɯnloÉ”ÇÇɹɥʇÊoɹ=Çuo=ɹnoÉŸuɯnloÉ”ÇÇɹɥʇÊoɹ-Çuo-(ɹnoÉŸuɯnloÉ”ÇÇɹɥʇoÊʇÊoɹ-ʇɥƃıÇ-ɹnoÉŸuɯnloÉ”xısÊoɹ-Çuo-)ɹnoÉŸuɯnloÉ”uÇÊŒÇsÊoɹ=Çuo=oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ-Çuo-oÊʇuɯnloÉ”xısɹnoÉŸÊoɹ=Çuo=ÇÇɹɥʇuɯnloÉ”ÇʌıɟÊoɹ-Çuo-ÇuıuuɯnloÉ”ÇʌıɟÊoɹ-uÇÊŒÇs-(ɹnoÉŸuɯnloÉ”xısÊoɹ-uÇÊŒÇs-ɹnoÉŸuɯnloÉ”ÇuoÊoɹ=uÇÊŒÇs=xısuɯnloÉ”ÇÇɹɥʇÊoɹ-uÇÊŒÇs-)ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ=uÇÊŒÇs=ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-(ɹnoÉŸuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-)ÇuouɯnloÉ”oÊʇÊoɹ=uÇÊŒÇs=ÇuouɯnloÉ”ÇuıuÊoɹ=ʇɥƃıÇ=ÇuouɯnloÉ”ÇʌıɟÊoɹ 'oÊʇuɯnloÉ”xısÊoɹ ÇuıuÊoÉ¹Ê‡É¥ÆƒÄ±Ç ÇÇɹɥʇuɯnloÉ”Çuo :ƃuıÊ-ɯ=ɹnoÉŸ=(ʇɥƃıÇ-ÇuouɯnloɔɹnoÉŸÊoɹ=ɹnoÉŸ=)oÊʇuɯnloÉ”xısÊoɹ-ɹnoÉŸ-ʇɥƃıÇuɯnloÉ”xısÊoɹ 'uÇÊŒÇsuɯnloÉ”xısÊoɹÇuıuuɯnloÉ”ÇʌıɟɹnoÉŸÊoɹ:slÉ-ɹnoÉŸ-ÇuıuuɯnloÉ”ÇuıuÊoɹ-ʇɥƃıÇ-(ÇuouɯnloÉ”uÇÊŒÇsÊoɹuÇÊŒÇsuɯnloÉ”ÇuıuÊoɹÇuıuuɯnloÉ”ÇʌıɟɹnoÉŸÊoɹ-ʇɥƃıÇ-)ÇuıuuɯnloÉ”uÇÊŒÇsÊoɹ 'ɹnoÉŸÊoɹÇÇɹɥʇ ÇÇɹɥʇÊoɹÇÇɹɥʇ :ƃuıÊ-x=ÇÇɹɥʇ=ʇɥƃıÇuɯnloɔɹnoÉŸÊoɹ 'ÇÇɹɥʇʞɔolqÇÇɹɥʇ xısuɯnloÉ”ÇÇɹɥʇ :É¥sıɟ ʇoqɹnʇ=ÇÇɹɥʇ=(ʇɥƃıÇ-ÇʌıɟuɯnloÉ”oÊʇÊoɹ=xıs=xısÇʌıɟuɯnloÉ”ÇuoÊoɹ-xıs-)uÇÊŒÇsuɯnloÉ”ÇuoÊoɹ=xıs=(uÇÊŒÇs-)uÇÊŒÇsuɯnloÉ”xısÊoɹ-xıs-(ÇuıuuɯnloÉ”ÇuıuÊoɹ 'ÇʌıɟÊoɹuÇÊŒÇs ÇÇɹɥʇÊoɹuÇÊŒÇs :ƃuıÊ-x=uÇÊŒÇs=ʇɥƃıÇuɯnloÉ”ÇʌıɟÊoɹ=xıs=ʇɥƃıÇuÇÊŒÇsuɯnloÉ”xısÊoɹ-xıs-)(Çuo-)ÇÇɹɥʇuɯnloÉ”xısÊoɹ=xıs=ÇuouɯnloÉ”ÇʌıɟÊoɹ-xıs-ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ=xıs=(uÇÊŒÇs-)xısuɯnloÉ”ÇÇɹɥʇÊoɹ-xıs-(Çuo-)xısuɯnloÉ”uÇÊŒÇsÊoɹ=xıs=ÇʌıɟuɯnloɔʇɥƃıÇÊoɹ-xıs-(uÇÊŒÇsÇÇɹɥʇ-xısuɯnloÉ”ÇuoÊoɹ=ɹnoÉŸ=xısuɯnloÉ”ÇuıuÊoɹ-ɹnoÉŸ-ɹnoÉŸuɯnloɔʇɥƃıÇÊoɹ=ɹnoÉŸ=)(ÇuıuuɯnloÉ”uÇÊŒÇsÇʌıɟÇÇɹɥʇÊoɹ-xıs-)ÇuıuuɯnloɔʇɥƃıÇÊoɹxıs
Ë™xıs=/=ÇuıuuɯnloɔʇɥƃıÇÊoɹ :uıÉɥɔ ƃuol ʇsÉl Çɥʇ Ë™uÇÊŒÇlÇ
Ë™xıs=/=ÇuıuuɯnloÉ”uÇÊŒÇsÊoɹʇɥƃıÇuɯnloÉ”xısÊoɹÇuıuuɯnloÉ”ÇʌıɟÊoɹʇɥƃıÇuɯnloÉ”oÊʇÊoɹÇʌıɟuɯnloÉ”ÇuoÊoɹÇuouɯnloÉ”oÊʇÊoɹÇÇɹɥʇuɯnloÉ”ÇuoÊoɹ <= ÇuıuuɯnloɔʇɥƃıÇʞɔolqÇuoÊoɹxısÊoɹÇuouɯnloÉ”\ʇɥƃıÇÊoɹuÇÊŒÇsuɯnloÉ”xısuɯnloɔɹnoɟʞɔolqÇÇɹɥʇÊoɹxıs ƃÉqɯɹınbs ʇuÉʇnɯ pÇuuıɟun ƃıq Ë™uÇʇ
Ë™xıs=/=uÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹxısuɯnloÉ”ÇÇɹɥʇÊoɹ :ÇuıuuɯnloɔʇɥƃıÇÊoɹxısuɯnloÉ”ÇuoÊoɹxısɹnoÉŸ ʇɥƃıÇʞɔolqxıs ʇɥƃıÇʞɔolqɹnoÉŸ :ƃuıÊ-Ê Çlqnop Ë™Çuıu
(ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ ÊoɹoÉŸ ÇnlÉÊŒ ou) uÇÊŒÇs=/=ÇuıuuɯnloɔʇɥƃıÇÊoɹ <= ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ-oÊʇ-ÇuouɯnloÉ”uÇÊŒÇsÊoɹ=oÊʇ=ÇuouɯnloɔɹnoÉŸÊoɹ-oÊʇ-ʇɥƃıÇuÇÊŒÇsuɯnloɔɹnoÉŸÊoɹ=oÊʇ=uÇÊŒÇsuɯnloÉ”ÇʌıɟÊoɹ=Çuıu=(ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ-Çuıu-ɹnoÉŸuɯnloÉ”uÇÊŒÇsÊoɹ=Çuıu=)ɹnoÉŸuɯnloÉ”ÇʌıɟÊoɹ=Çuo=ɹnoÉŸuɯnloÉ”uÇÊŒÇsÊoɹ-Çuo-oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ=Çuo=ÇÇɹɥʇuɯnloÉ”ÇuıuÊoɹ-Çuo-ÇÇɹɥʇuɯnloÉ”xısÊoɹ=Çuo=ÇʌıɟuɯnloÉ”xısÊoɹ-Çuo-(ɹnoÉŸuɯnloÉ”ÇÇɹɥʇÊoɹ-Çuo-)ÇʌıɟuɯnloÉ”ÇÇɹɥʇÊoɹ 'ʇɥƃıÇuɯnloÉ”oÊʇÇuoÊoɹoÊʇ :ƃuıÊ-x pÇuuıɟ=oÊʇ=(oÊʇ-ÇuouɯnloÉ”ÇʌıɟÊoɹ=xıs=ÇÇɹɥʇuɯnloÉ”xısÇʌıɟÊoɹ-xıs-)ÇÇɹɥʇuɯnloÉ”ÇuoÊoɹ=xıs=ÇʌıɟuɯnloÉ”ÇuoÊoɹ=ÇÇɹɥʇ=ÇʌıɟuɯnloÉ”oÊʇÊoɹ-ÇÇɹɥʇ-(oÊʇ-ÇÇɹɥʇuɯnloɔʇɥƃıÇÊoɹ=ÇÇɹɥʇ=ÇuouɯnloÉ”uÇÊŒÇsÊoɹ-ÇÇɹɥʇ-ÇuıuuɯnloÉ”uÇÊŒÇsÊoɹ=ÇÇɹɥʇ=ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ-ÇÇɹɥʇ-)(ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ-xıs-ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ=xıs=)ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-xıs-ʇɥƃıÇuɯnloÉ”xısÊoɹ-ɹnoÉŸ-(ÇʌıɟuɯnloÉ”ÇÇɹɥʇÊoɹ 'xısÊoÉ¹Ê‡É¥ÆƒÄ±Ç oÊʇÊoÉ¹Ê‡É¥ÆƒÄ±Ç :ƃuıÊ-x pÇuuıɟ=ʇɥƃıÇ=)(Çuo-)oÊʇuɯnloÉ”xısÊoɹ=ɹnoÉŸ=(ʇɥƃıÇ-)oÊʇuɯnloÉ”oÊʇÊoɹ=uÇÊŒÇs=(xısÇÇɹɥʇ-uÇÊŒÇsuɯnloÉ”ÇuoÊoɹ=uÇÊŒÇs=)ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-(ÇuıuoÊʇ-)ʇɥƃıÇuɯnloÉ”ÇʌıɟÊoɹ=uÇÊŒÇs=ʇɥƃıÇuÇÊŒÇsuɯnloÉ”xısÊoɹ-uÇÊŒÇs-(ʇɥƃıÇuɯnloÉ”xısÊoɹɹnoÉŸuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-)(ʇɥƃıÇÇuo-)ɹnoÉŸuɯnloÉ”xısÊoɹ=uÇÊŒÇs=xısuɯnloÉ”ÇʌıɟÊoɹ-uÇÊŒÇs-(ʇɥƃıÇuɯnloÉ”xısÊoɹ-ÇÇɹɥʇ-uÇÊŒÇsuɯnloÉ”xısÊoɹ-xıs-(ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ-xıs-)(ÇÇɹɥʇ-)uÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹ=xıs=ÇuıuʇɥƃıÇuÇÊŒÇsuɯnloÉ”uÇÊŒÇsÊoɹ-xıs-xısuɯnloÉ”uÇÊŒÇsÊoɹ=xıs=xısuɯnloɔɹnoÉŸÊoɹ=ÇÇɹɥʇ=)(xıs-)xısuɯnloÉ”ÇÇɹɥʇÊoɹ=uÇÊŒÇs=ÇuouɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-(ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ-uÇÊŒÇs-)(oÊʇ-)ÇuouɯnloÉ”ÇuıuÊoɹ=uÇÊŒÇs=oÊʇuɯnloɔʇɥƃıÇÊoɹ-uÇÊŒÇs-(ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ-uÇÊŒÇs-)(oÊʇuɯnloÉ”ÇuoÊoɹ-ɹnoÉŸ-(xısÇÇɹɥʇ-)xısuɯnloÉ”ÇuoÊoɹ=ɹnoÉŸ=xısuɯnloÉ”ÇuıuÊoɹ-ɹnoÉŸ-(ÇuıuoÊʇ-)ɹnoÉŸuɯnloɔʇɥƃıÇÊoɹ=ɹnoÉŸ=)ÇuıuuɯnloɔʇɥƃıÇÊoɹuÇÊŒÇs
Ë™uÇÊŒÇs=/=ÇuıuuɯnloɔʇɥƃıÇÊoɹ :uıÉɥɔ ƃuol ɹÇɥʇouÉ Ê‡ÇÊŽ puÉ Ë™Ê‡É¥ÆƒÄ±Ç
(Ê‡É¥ÆƒÄ±Ç ÊžÉ”olq uı Çuo ɹoÉŸ ÇÉ”Éld ou) uÇÊŒÇs=/=xısuɯnloÉ”ÇuoÊoɹ <= ÇʌıɟuɯnloÉ”ÇuıuÊoɹ-Çuo-ÇʌıɟuɯnloÉ”xısÊoɹ=Çuo=oÊʇuɯnloÉ”xısÊoɹ-Çuo-(xısɹnoÉŸuɯnloÉ”uÇÊŒÇsÊoɹ-Çuo-)oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ=Çuo=ÇÇɹɥʇuɯnloÉ”ÇuıuÊoɹ=Çuıu=oÊʇuɯnloɔʇɥƃıÇuÇÊŒÇsÊoɹ-Çuıu-oÊʇuɯnloÉ”ÇÇɹɥʇÊoɹ 'xısÊoÉ¹Ê‡É¥ÆƒÄ±Ç oÊʇÊoÉ¹Ê‡É¥ÆƒÄ±Ç :É¥sıɟ ʇoqɹnʇ=ʇɥƃıÇ=(Çuo-)ÇÇɹɥʇuɯnloÉ”xısÊoɹ=xıs=uÇÊŒÇsuɯnloÉ”xısÊoɹ-xıs-uÇÊŒÇsuɯnloÉ”ÇuoÊoɹ=xıs=(ʇɥƃıÇ-ɹnoÉŸuɯnloÉ”oÊʇÊoɹ=ɹnoÉŸ=(oÊʇuɯnloÉ”ÇÇɹɥʇÊoɹ 'ʇɥƃıÇÊoɹoÊʇ ÇuoÊoɹoÊʇ :É¥sıɟ ʇoqɹnʇ=oÊʇ=oÊʇuɯnloÉ”ÇuoÊoɹ=ɹnoÉŸ=)ÇuouɯnloÉ”oÊʇÊoɹ-ɹnoÉŸ-ÇuouɯnloɔɹnoÉŸÊoɹ=ɹnoÉŸ=oÊʇuɯnloÉ”xısÊoɹ-ɹnoÉŸ-ʇɥƃıÇuɯnloÉ”xısÊoɹ-ÇÇɹɥʇ-)(oÊʇ-ÇʌıɟuɯnloÉ”ÇuoÊoɹ=ÇÇɹɥʇ=ÇʌıɟuɯnloÉ”oÊʇÊoɹ-ÇÇɹɥʇ-)ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-xıs-(ʇɥƃıÇuɯnloÉ”xısÊoɹ-xıs-)ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ=xıs=ÇuıuuɯnloÉ”uÇÊŒÇsÊoɹ=ÇÇɹɥʇ=ÇuıuuɯnloɔɹnoÉŸÊoɹ-ÇÇɹɥʇ-xısuɯnloɔɹnoÉŸÊoɹ=ÇÇɹɥʇ=xısuɯnloÉ”ÇÇɹɥʇÊoɹ=xıs=ÇʌıɟuɯnloÉ”oÊʇÇuoÊoɹ-xıs-(oÊʇ-)ÇʌıɟuɯnloɔʇɥƃıÇÊoɹ=xıs=(ʇɥƃıÇɹnoÉŸ-oÊʇuɯnloÉ”oÊʇÊoɹ=uÇÊŒÇs=(xısÇÇɹɥʇ-ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ=uÇÊŒÇs=)ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ-uÇÊŒÇs-ÇuouɯnloÉ”ÇuıuÊoɹ=uÇÊŒÇs=oÊʇuɯnloɔʇɥƃıÇÊoɹ-uÇÊŒÇs-)(ÇuıuoÊʇ-ÇÇɹɥʇuɯnloɔʇɥƃıÇÊoɹ=ÇÇɹɥʇ=)uÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹ=uÇÊŒÇs=uÇÊŒÇsuɯnloÉ”xısÊoɹ-uÇÊŒÇs-(ʇɥƃıÇuɯnloÉ”xısÊoɹ-uÇÊŒÇs-)(ʇɥƃıÇÇuo-)ɹnoÉŸuɯnloÉ”xısÊoɹ=uÇÊŒÇs=xısuɯnloÉ”ÇʌıɟÊoɹ-uÇÊŒÇs-(xısÇÇɹɥʇ-ÇuıuÇÇɹɥʇuɯnloɔʇɥƃıÇÊoɹ=ɹnoÉŸ=ɹnoÉŸuɯnloɔʇɥƃıÇÊoɹ-ɹnoÉŸ-(Çuo-)xısuɯnloÉ”ÇuıuÊoɹ=ɹnoÉŸ=)(xısuɯnloÉ”ÇÇɹɥʇÊoɹuÇÊŒÇsoÊʇuɯnloÉ”ÇuoÊoɹ-uÇÊŒÇs-)(ÇÇɹɥʇ-)xısuɯnloÉ”ÇuoÊoɹuÇÊŒÇs
Ë™uÇÊŒÇs=/=xısuɯnloÉ”ÇuoÊoɹ :uıÉɥɔ ƃuol ɹÇɥʇouÉ Ê‡ÇÊŽ Ë™uÇÊŒÇs
(ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ ɹoÉŸ ÇnlÉÊŒ ou) ÇÇɹɥʇ=/=xısuɯnloÉ”ÇuoÊoɹ <= ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ-oÊʇ-ÇuouɯnloÉ”ÇuıuÊoɹ=oÊʇ=ÇuouɯnloÉ”ÇʌıɟɹnoÉŸÊoɹ-oÊʇ-oÊʇuɯnloɔɹnoÉŸÊoɹ-Çʌıɟ-xısuɯnloɔɹnoÉŸÊoɹ-Çuo-(oÊʇuɯnloɔɹnoÉŸÊoɹ-ʇɥƃıÇ-ÇuıuuɯnloɔɹnoÉŸÊoɹ-Çuo-)(ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ-Çuıu-ÇʌıɟuɯnloÉ”ÇuıuÊoɹ=Çuıu=)ÇʌıɟuɯnloɔɹnoÉŸÊoɹ=Çuo=xısuɯnloÉ”ÇʌıɟɹnoÉŸÊoɹ-Çuo-xısuɯnloÉ”uÇÊŒÇsÊoɹ=Çuo=oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ-Çuo-(oÊʇuɯnloɔɹnoÉŸÊoɹ-Çuo-)oÊʇuɯnloÉ”xısÊoɹ=Çuo=ɹnoÉŸuɯnloÉ”xısÊoɹ-Çuo-(ɹnoÉŸuɯnloÉ”uÇÊŒÇsxısÇʌıɟÊoɹ-Çuo-)ɹnoÉŸuɯnloÉ”ÇÇɹɥʇÊoɹ 'xısÊoÉ¹Ê‡É¥ÆƒÄ±Ç oÊʇÊoÉ¹Ê‡É¥ÆƒÄ±Ç :É¥sıɟ ʇoqɹnʇ=ʇɥƃıÇ=(ɹnoÉŸuɯnloÉ”ÇÇɹɥʇÊoɹ 'ʇɥƃıÇÊoɹoÊʇ ÇuoÊoɹoÊʇ :É¥sıɟ ʇoqɹnʇ=oÊʇ=)oÊʇuɯnloÉ”ÇuoÊoɹ=ɹnoÉŸ=oÊʇÇuouɯnloÉ”oÊʇÊoɹ-ɹnoÉŸ-(ʇɥƃıÇ-)ɹnoÉŸuɯnloÉ”oÊʇÊoɹ=ɹnoÉŸ=(oÊʇ-)ɹnoÉŸuɯnloÉ”ÇuoÊoɹ=uÇÊŒÇs=ɹnoÉŸuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-(ÇuouɯnloÉ”oÊʇÊoɹ=xıs=ÇÇɹɥʇuɯnloÉ”oÊʇÇuoÊoɹ-xıs-(ʇɥƃıÇÇuo-)ÇÇɹɥʇuɯnloÉ”xısÊoɹ=xıs=ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ-uÇÊŒÇs-)(xıs-)ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ=uÇÊŒÇs=uÇÊŒÇsuɯnloÉ”ÇuoÊoɹ-uÇÊŒÇs-(xıs-)uÇÊŒÇsuɯnloÉ”xısÊoɹ=uÇÊŒÇs=(xıs-)ʇɥƃıÇuɯnloɔɹnoÉŸÊoɹ=ɹnoÉŸ=(ÇuouɯnloɔɹnoÉŸÊoɹ=ɹnoÉŸ=)ʇɥƃıÇuɯnloɔɹnoÉŸÊoɹ=ÇÇɹɥʇ=(ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-ÇÇɹɥʇ-)ÇuıuuɯnloɔɹnoÉŸÊoɹ-ÇÇɹɥʇ-ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ-uÇÊŒÇs-ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ-xıs-(ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ-xıs-)(ɹnoÉŸuɯnloÉ”xısÊoɹ-uÇÊŒÇs-xısuɯnloÉ”ÇʌıɟÊoɹ=uÇÊŒÇs=)xısuɯnloÉ”ÇÇɹɥʇÊoɹ=xıs=ÇʌıɟuɯnloÉ”oÊʇÇuoÊoɹ-xıs-(oÊʇ-oÊʇuɯnloɔʇɥƃıÇÊoɹ=uÇÊŒÇs=)(ÇuıuoÊʇ-)ÇʌıɟuɯnloɔʇɥƃıÇÊoɹ=xıs=(ÇuıuuɯnloɔɹnoÉŸÊoɹ-ɹnoÉŸ-)(uÇÊŒÇs-)ÇuıuuɯnloɔʇɥƃıÇÊoɹ=ɹnoÉŸ=ɹnoÉŸuɯnloɔʇɥƃıÇÊoɹ-ɹnoÉŸ-(uÇÊŒÇs-)(ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ-ɹnoÉŸ-)xısuɯnloÉ”ÇuıuÊoɹ=ɹnoÉŸ=(ʇɥƃıÇ-ÇÇɹɥʇuɯnloÉ”oÊʇÊoɹ=ÇÇɹɥʇ=(oÊʇ-)ÇuouɯnloÉ”uÇÊŒÇsÊoɹ=ÇÇɹɥʇ=ÇÇɹɥʇuɯnloɔʇɥƃıÇÊoɹ-ÇÇɹɥʇ-(uÇÊŒÇsxıs-)uÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹ=ÇÇɹɥʇ=uÇÊŒÇsuɯnloÉ”xısÊoɹ-ÇÇɹɥʇ-(ʇɥƃıÇuɯnloÉ”xısÊoɹ-ÇÇɹɥʇ-)(ʇɥƃıÇÇuo-)ÇʌıɟuɯnloÉ”xısÊoɹ=ÇÇɹɥʇ=ÇʌıɟuɯnloÉ”oÊʇÇuoÊoɹ-ÇÇɹɥʇ-)(uÇÊŒÇsxısɹnoÉŸ-)(xısuɯnloɔɹnoÉŸÊoɹuÇÊŒÇsÇÇɹɥʇuɯnloÉ”ÇuoÊoɹ-ÇÇɹɥʇ-)xısuɯnloÉ”ÇuoÊoɹÇÇɹɥʇ
Ë™ÇÇɹɥʇ=/=xısuɯnloÉ”ÇuoÊoɹ :uıÉɥɔ ƃuol ɹÇɥʇouÉ Ë™xıs
(oÊʇuɯnloɔɹnoÉŸÊoɹ ɹoÉŸ ÇnlÉÊŒ ou) ÇÇɹɥʇ=/=ÇuıuuɯnloɔʇɥƃıÇÊoɹ <= oÊʇuɯnloɔɹnoÉŸÊoɹ-Çʌıɟ-xısuɯnloɔɹnoÉŸÊoɹ-Çuo-ɹnoÉŸuɯnloÉ”xısÊoɹ-ʇɥƃıÇ-(oÊʇuɯnloɔɹnoÉŸÊoɹ-ʇɥƃıÇ-)oÊʇuɯnloÉ”xısÊoɹ-Çuo-(oÊʇuɯnloɔɹnoÉŸÊoɹ-Çuo-)oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ-oÊʇ-ʇɥƃıÇuɯnloÉ”uÇÊŒÇsÊoɹ=oÊʇ=ʇɥƃıÇuɯnloÉ”ÇʌıɟÊoɹ-oÊʇ-(oÊʇuɯnloɔɹnoÉŸÊoɹ-oÊʇ-)ÇuouɯnloÉ”ÇʌıɟÊoɹ-xıs-ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ-uÇÊŒÇs-ÇuıuuɯnloÉ”ÇÇɹɥʇÊoɹ=uÇÊŒÇs=ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ-ɹnoÉŸ-ʇɥƃıÇuɯnloÉ”xısÊoɹ=ɹnoÉŸ=(ÇuouɯnloÉ”xısÊoɹ=ɹnoÉŸ=)oÊʇuɯnloÉ”xısÊoɹ-ɹnoÉŸ-oÊʇuɯnloÉ”oÊʇÊoɹ 'xısÊoÉ¹Ê‡É¥ÆƒÄ±Ç oÊʇuɯnloɔɹnoÉŸ ɹnoÉŸuɯnloÉ”oÊʇÊoɹ :ƃuÄ±Ê pıɹqÊŽÉ¥=ʇɥƃıÇ=ÇÇɹɥʇuɯnloÉ”xısÊoɹ-ʇɥƃıÇ-(ÇuouɯnloÉ”ÇʌıɟÊoɹ-ʇɥƃıÇ-ÇuouɯnloÉ”ÇuıuÊoɹ=ʇɥƃıÇ=ÇÇɹɥʇuɯnloÉ”ÇuıuÊoɹ-ʇɥƃıÇ-)(oÊʇuɯnloÉ”oÊʇÊoɹ-ʇɥƃıÇ-)ÇÇɹɥʇuɯnloÉ”ÇÇɹɥʇÊoɹ-Çuıu-(oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ-Çuıu-)oÊʇuɯnloÉ”ÇÇɹɥʇÊoɹ=Çuıu=oÊʇuɯnloÉ”uÇÊŒÇsÊoɹ 'ʇɥƃıÇuɯnloÉ”Çuıu ɹnoÉŸuɯnloÉ”Çuıu :ƃuıÊ-x=Çuıu=ʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ'ÇuıuʇɥƃıÇuɯnloÉ”ÇuıuÊoɹ:sÉ¥É=uÇÊŒÇs=uÇÊŒÇsuɯnloÉ”ÇuıuʇɥƃıÇÊoɹ-uÇÊŒÇs-uÇÊŒÇsuɯnloÉ”xısÊoɹ=uÇÊŒÇs=ɹnoÉŸuɯnloÉ”xısÊoɹ-uÇÊŒÇs-(ÇÇɹɥʇuɯnloÉ”ÇÇɹɥʇÊoɹ 'ɹnoÉŸÊoɹoÊʇ ʇɥƃıÇÊoɹoÊʇ :É¥sıɟ ʇoqɹnʇ=oÊʇ=)(ɹnoÉŸuɯnloÉ”oÊʇÊoɹ-uÇÊŒÇs-)ɹnoÉŸuɯnloÉ”ÇuoÊoɹ=uÇÊŒÇs=uÇÊŒÇsuɯnloÉ”ÇuoÊoɹ=ÇÇɹɥʇ=ʇɥƃıÇuɯnloÉ”oÊʇÊoɹ-ÇÇɹɥʇ-(oÊʇ-)ʇɥƃıÇuɯnloɔɹnoÉŸÊoɹ=ÇÇɹɥʇ=ʇɥƃıÇuÇÊŒÇsuɯnloÉ”xısÊoɹ-ÇÇɹɥʇ-ÇʌıɟuɯnloÉ”xısÊoɹ=ÇÇɹɥʇ=ÇʌıɟuɯnloÉ”oÊʇÇuoÊoɹ-ÇÇɹɥʇ-(xısuɯnloɔɹnoÉŸÊoɹ-ÇÇɹɥʇ-)(oÊʇuɯnloÉ”oÊʇÇuoÊoɹ-uÇÊŒÇs-(ÇuıuoÊʇ-)oÊʇuɯnloɔʇɥƃıÇÊoɹ=uÇÊŒÇs=(oÊʇ-)uÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹ=xıs=ÇʌıɟuɯnloɔʇɥƃıÇÊoɹ-xıs-(xısuɯnloÉ”ÇʌıɟÊoɹ=uÇÊŒÇs=)(oÊʇÇuouɯnloÉ”uÇÊŒÇsÊoɹ-ʇɥƃıÇ-ÇuıuuɯnloÉ”uÇÊŒÇsÊoɹ-xıs-)xısuɯnloÉ”uÇÊŒÇsÊoɹ=xıs=(uÇÊŒÇs-)(oÊʇuɯnloÉ”ÇuoÊoɹ-ɹnoÉŸ-)xısuɯnloÉ”ÇuoÊoɹ=ɹnoÉŸ=)(uÇÊŒÇsxıs-)(ÇÇɹɥʇuɯnloÉ”ÇÇɹɥʇÊoɹ-ÇÇɹɥʇ-)xısuɯnloÉ”ÇÇɹɥʇÊoɹ=ÇÇɹɥʇ=ÇuouɯnloÉ”ÇÇɹɥʇÊoɹ-ÇÇɹɥʇ-ÇuouɯnloÉ”uÇÊŒÇsÊoɹ=ÇÇɹɥʇ=ÇÇɹɥʇuɯnloɔʇɥƃıÇÊoɹ-ÇÇɹɥʇ-(ÇuıuuɯnloÉ”uÇÊŒÇsÇÇɹɥʇÊoɹ-ÇÇɹɥʇ-)(uÇÊŒÇsxıs-)(ɹnoÉŸuɯnloÉ”oÊʇÇuoÊoɹ-ɹnoÉŸ-(oÊʇ-)ɹnoÉŸuɯnloɔʇɥƃıÇÊoɹ=ɹnoÉŸ=)ÇuıuuɯnloɔʇɥƃıÇÊoɹÇÇɹɥʇ
Ë™ÇÇɹɥʇ=/=ÇuıuuɯnloɔʇɥƃıÇÊoɹ :uıÉɥɔ ƃuol ʇsɹıɟ Çɥʇ Ë™Çʌıɟ
Ë™uÇÊŒÇsxısÇÇɹɥʇ=/=ÇʌıɟɹnoÉŸÇÇɹɥʇoÊʇuɯnloÉ”ÇÇɹɥʇÊoɹ <= ÇÇɹɥʇÊoɹuÇÊŒÇsxısÇÇɹɥʇ ʇÇldıɹʇ pÇÊžÉu ˙ɹnoÉŸ
Ë™Çuo=uÇÊŒÇsuɯnloÉ”oÊʇÊoɹ Çlƃuıs pÇÊžÉu Ë™ÇÇɹɥʇ
Ë™uÇÊŒÇsxısÇÇɹɥʇ=/=uÇÊŒÇsuɯnloÉ”ÇuıuuÇÊŒÇsÇʌıɟɹnoÉŸoÊʇÊoɹ <= uÇÊŒÇsuɯnloÉ”uÇÊŒÇsxısÇÇɹɥʇ ʇÇldıɹʇ pÇÊžÉu Ë™oÊʇ
ÇuıuoÊʇ=/=ÇuıuuÇÊŒÇsuɯnloɔʇɥƃıÇÊoɹ 'ʇɥƃıÇÇuo=/=ʇɥƃıÇuÇÊŒÇsuɯnloÉ”xısÊoɹ 'ÇʌıɟÇuo=/=xısuɯnloÉ”ÇÇɹɥʇÇuoÊoɹ 'ʇɥƃıÇoÊʇ=/=ÇuouɯnloÉ”ÇÇɹɥʇoÊʇÊoɹ 'uÇÊŒÇs=/=ɹnoÉŸuɯnloÉ”ÇʌıɟÊoɹ 'ÇÇɹɥʇ=/=ÇʌıɟuɯnloɔɹnoÉŸÊoɹ 'xıs=/=ÇÇɹɥʇuɯnloÉ”ÇʌıɟÊoɹ 'ɹnoÉŸ=/=oÊʇuɯnloɔɹnoÉŸÊoɹ :suoıʇÉuıɯılÇ
ÇʌıɟɹnoÉŸÇÇɹɥʇoÊʇuɯnloɔʇɥƃıÇÊoɹ 'ÇʌıɟɹnoÉŸÇÇɹɥʇoÊʇuɯnloÉ”xısÊoɹ 'xısuɯnloÉ”ÇuıuuÇÊŒÇsÇʌıɟɹnoÉŸÊoɹ 'ÇuouɯnloɔʇɥƃıÇuÇÊŒÇsÇʌıɟɹnoÉŸÊoɹ dool Êžs Ë™Çuo
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