暴婊晛‫ؙٗ‬ٝ‫ؙ؎ت‬‫ך‬䧭⸆桦‫ח‬ꟼ‫׷ׅ‬㹋꿀涸鐰⣣ᇓओ நዒ, ºෆ๖ ་᎓၍౨ೂ་ॺᇌँගሇॺᆪ涪邌‫ך‬圓䧭
1. ଞ੄გ૤• ‫֧֮פי׵بآפ‬• ‫֭פי׵بآפ‬ถୱጴ֧֮

2. ৘ᎌଞ੄• ‫֭פי׵بآפ‬૱్ᆷ఺֔

3. ଞ੄ኬ࿨4. ࿓ࡎ೚ሓ• ၟ೜ᄟ‫֭פי׵بآפ‬࿊ਟ• ૱్৿‫ءؚؔ׬‬՛‫֭ب؜׬‬ሑሓ

5. ಲଫଅऐ֧ணళ• ૱్৿‫ءؚؔ׬‬՛‫֭ب؜׬‬ଅऐ

6. ֽ֧‫֧׀‬ௗଢ଼֭ड༎ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-112

1. 灇瑔胜兝‫ؙٗ‬ٝ‫כהؙ؎ت‬• ‫ࡴ֧֮חט׻؟ײ‬෗ዥֲዿ֭‫נ‬՛‫ק׾‬՛֭ؕຳൺ• ‫ࡴ֭חט׻؟ײ֮פי׵بآפ‬೟

Solitaire for Windows 3.1[https://archive.org/details/win3_solwin]
Microsoft Solitaire Collection(Microsoft Windows 10)ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-113‫ؙٗ‬ٝ‫כהؙ؎ت‬• ቎጖֭‫ؠ‬՛‫֦֮ؠ‬牞椙‫ّ֦٭أ‬ց‫׊‬• ഷৼඡ໺֪։փ֥ӣጮ୶֌֭‫נ‬՛‫֋׾‬ໜఓ֘‫׊‬• ጮ୶֌֭‫נ‬՛‫פب؞֮׾‬ӡ෾ಌӢ‫׮׃‬՛‫׽‬ӡ‫سحخذ‬Ӣ֋ᇀ֊‫֩׈‬փ• ،‫נ֧׊׀ුביء‬՛‫ב׾‬ᅳ֪֦֌‫׊‬• ࡴ෗‫ק‬՛ؕ (؆‫֦ )ؠׯ‬ց‫׊‬• փ֎֣֊֭৘ᎌଞ੄ӣ։‫ֲׇ‬቎브֦֮牞㴻‫ّ٭أ‬֧֖֥࠿օ• ഷৼඡ໺֪։փ֥ӣָ֥֭֘‫נ‬՛‫ב׾‬ᅳ୶֌֪ᇖָ‫׊‬• ֭֒‫ׇ‬օ֩็࿊֭‫פי׵بآפ‬ӡ‫חט׻؟ײ‬Ӣ‫ב‬“Thoughtful Solitaire” ֧ାֵ [Yan+04][Yan+04] Xiang Yan, Persi Diaconis, Paat Rusmevichientong, Benjamin Van Roy: "Solitaire: Man Versus
Machine". Advances in Neural Information Processing Systems 17 (NIPS 2004): 1553-1560
ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-114‫ؙٗ‬ٝ‫כהؙ؎ت‬氠靣• ຎష (suit stacks)

㻗動篁動• ‫ פ׸״׮‬x 4• ඘ష (build stacks)• ‫ פ׸״׮‬x 7• ౅ష (pile & talon)㖪動• ጮ୶֌‫ פ׸״׮‬x 1• ᅳ୶֌‫ פ׸״׮‬x 1

ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-115‫ؙٗ‬ٝ‫כהؙ؎ت‬㻗動篁動⮴劻枱䡢 埉徙溷‫עמ‬• ຎష֭‫ָ֥֮֘פ׸״׮‬઱• ඘ష֭२‫֭פ׸״׮‬቙෾֮ӣ
1, 2, …, 7 ቙ (૱28቙)• ౖ‫נ֭׉‬՛‫( ׾‬52-28=24቙) ֮ӣ౅ష֭ጮ୶֌‫ֿู֪פ׸״׮‬㖪動‫סّ٭أ‬潨溷• ָ֥֭֘‫נ‬՛‫ב׾‬ຎష֪ࡤ၌֘‫׊‬• ֖֞֟ӣ‫נ‬՛‫ࡤ֭׾‬၌֮ଢ଼ഠ֭‫ؠ‬՛‫֦ऀ֭ؠ‬։֒֩օຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-11

6‫ؙٗ‬ٝ‫כהؙ؎ت‬㻗動• ඘ష֭ (ᅋ઱֭) ‫֮פ׸״׮‬ӣ๐၈֪զ‫׬‬՛‫׮بצ‬է֧‫׊׋ׇ֯‬ӣࡴ࿊֭ඞଉ‫ב‬ተ֞֘‫נ‬՛‫׾‬፿‫ב‬৞ֿ篁動㖪動• զ‫آ٭ب‬٤‫ت‬է֧֮ӣ• ๐၈֊‫׈‬ቨᅐֽ֦ӣ‫֋פب؞‬൦വ֪ᎌ໗֖֥փ‫׊‬• ፥ไ֘‫נ׊‬՛‫׊֩ࡣ֮׾‬නӡ‫֮خذ‬฾ӣ‫֮سح‬ோӢ‫ב‬ಏ֣• ‫׬‬՛‫ ֮֔ྙ֭׮بצ‬1 ࡒඑ‫ऀࡒྙפ׸״׮‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-117‫‪㻗動‬‬‫‪篁動‬‬‫כהؙ؎ت‪ٗٝ‬ؙ‬‫‪է‬ت‪٤‬آ٭ب‪• զ‬‬‫‪㖪動‬‬‫‪֋൦വ֪ᎌ໗‬פب؞ •‬‫ׁ֣ב‪න‬׊֩ࡣ֮׾‪՛‬נ‪• ፥ไ‬‬‫‪J‬ر‬‫‪6‬ر‬‫‪10‬س‬‫‪5‬س‬‫‪9‬د‬‫‪4‬د‬‫‪፯Ӣ‬‬‫‪ቨᅐ‬‬‫‪๐၈‬‬‫‪3‬س‬‫֌୶‪֮ጮ‬׾‪՛‬נ‪֦֩փ‬׮بצ‪՛‬׬‪֦֮ӣ‬פי׵بآפ֭‪ͤྫྷඛ‬‬‫‪8‬‬‫‪༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-11‬׽פל׭آ‪،‬ؠׯ‪՛ؕ؆‬ק֚‪ຎ஽‬‬㻗動‫ؙٗ‬ٝ‫כהؙ؎ت‬‫غ٭؜‬瓌ⳛ‫ס‬ٜ‫٭‬ٜ篁動㖪動• ౅ష֊‫ࡤ֭׈‬၌• ᅳ୶֌‫ ֭פ׸״׮‬1 ᄮඑ֭ 1 ቙֭‫ב־‬໢֭౅ַࡤ၌֚֔‫֧֒׊‬֋֦֌‫׊‬• ጮ୶֌‫׈֊פ׸״׮‬ᅳ୶֌‫ַפ׸״׮‬ӣ 3 ቙֣֙ࡤ၌֚֔‫֧֒׊‬֋֦֌‫׊‬ӡզᇸഊէӢ• ጮ୶֌‫֋פ׸״׮‬઱֪֢֩֞‫׈‬ӣᅳ୶֌‫׀ָֽ֧֥֘בפ׸״׮‬֥ጮᇪ֖ӣጮ୶֌‫֪פ׸״׮‬኱֧֘֒֋֦֌‫׊‬ӡզ֎֙֔‫׈‬փէӢ• ඘ష֊‫ࡤ֭׈‬၌• ඘ష֭ 7 ֣֭౅֭օ֠ӣ‫׬‬՛‫( ׮بצ‬๺໲ֽ֮֞๐၈‫ב‬৞ֿᆪᇀ፿) ‫ב‬໢֭౅ַࡤ၌֚֔‫׊֌֦֋֧֒׊‬• ֖֞֟ӣಲ఑֪ࡤ၌֦֌‫֭֮׊‬ӣࡤ၌๐֭౅֋‫נ‬՛‫׾‬ӡ‫נ‬՛‫׾‬፿Ӣ‫ב‬೥ጫ֘‫׊‬඘஽֭‫־‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-119‫‪㻗動‬‬‫‪篁動‬‬‫כהؙ؎ت‪ٗٝ‬ؙ‬‫׀‪ٜ 籽‬٭‪ٜ‬סⳛ‪瓌‬غ٭؜‬‫‪㖪動‬‬‫֭֮׊֘‪• ຎష֋೥ጫ‬‬‫‪೥ጫ‬ב־֭׾‪՛‬נ֭׽‪՛‬׮֞׋׈׀‪֧֪֓ଂ‬פ׸״׮‪• २‬‬‫֣ ‪֋ 1‬פب؞֦׽‪՛‬׮֗‪ (၍‬׊֘‪֧፥ไ‬׾‪՛‬נ‪֭๐၈‬פ׸״׮‪• २‬‬‫‪೥ጫ‬ב־֭׾‪՛‬נ )‪་֌փ‬‬‫‪೥ጫ‬ב־֭ )פب؞‪, ௻൚‬׮‪՛‬ם( ‪֋઱֧֭֌֮ A‬פ׸״׮ •‬‫֭֮׊֘‪• ඘ష֋೥ጫ‬‬‫ࡤ֩‪օ‬ׇ׊֩֎ྙ֋‪է‬׮بצ‪՛‬׬‪৞ֿզ‬ב׾‪՛‬נ‪֭๐၈‬פ׸״׮‪• २‬‬‫‪೥ጫ‬ב‪၌‬‬‫‪؋‬׾‪՛‬נֿ‪৞‬ב )פب؞‪, ௻་‬ץبע( ‪֋઱֧֭֌֮ K‬פ׸״׮ •‬‫‪೥ጫ‬ב־֭פ׸آ‬‫֢֪֩‪֋઱‬׮بצ‪՛‬׬֭פ׸״׮ׇ֥֢֪‪֭ࡤ၌‬׈֊‪• ඘ష‬‬‫׊֧֘׮بצ‪՛‬׬֪֞‪ශ‬ב‪֭๐၈ 1 ቙‬פ׸״׮‪֞඘஽֮ӣ‬‬‫‪10‬‬‫‪༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-11‬׽פל׭آ‪،‬ؠׯ‪՛ؕ؆‬ק֚‪ຎ஽‬‬‫ؙٗ‬ٝ‫ךؙ؎ت‬䧭⸆桦‫כה‬• ይև‫֞׋׈‬ഷৼვམ֊‫׈‬ถୱඡ໺֪ြ༥֦֌‫֌֧׊‬ӣ֭֜ഷৼვམ֮䧯Ⲍ⺪茣֧փօ• ถୱඡ໺ = ָ֥֭֘‫נ‬՛‫ב׾‬ຎష֪ࡤ၌֚֔֞ඡ໺• ਲ਼֪ӣይև‫֞׋׈‬ഷৼვམ֊‫ׇ֭֮֨׈‬օ֪،‫ׁ֥֖יء‬ถୱඡ໺֪ြ༥֦֌֩փ֧֌ӣ֭֜ഷৼვམ֮䧯Ⲍ┮茣֧փօ• ‫֪ؕ׵ب؞‬ይև‫֞׋׈‬ഷৼვམ‫ב‬ภถ֘‫֌֧׊‬ӣถୱईႷ֩ഷৼვམ֋ၜ‫׊׋׈‬॰ጴ‫ב‬‫֭פי׵بآפ‬䧯Ⲍ椙֧‫ֵׇ‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1111‫ؙٗ‬ٝ‫ךؙ؎ت‬䧭⸆桦‫כה‬• ᅮമ࿨֩‫נ‬՛‫ב׾‬ዿփ‫֧׊‬ӣ‫֭פי׵بآפ‬ईႷ֩ഷৼვམ֮ӡࡴ֮ࣤӢ࿊෾଼• 52! ~ 8.1 x 1067 ྫྷ‫׉‬• ‫֭פי׵بآפ‬ถୱጴ֮࿊෾
• Yan ‫[ ׈‬Yan+04] ֪‫֯׋ׇ‬ӣզ‫חט׻؟ײ‬ӡ‫פי׵بآפ‬Ӣ֭ถୱጴ‫ב‬ଂ࿊֦֌֩փ֭֮ࣤዿ෾ॺ֭ན֭ࡴ֣֦ց‫׊‬է[Yan+04] Xiang Yan, Persi Diaconis, Paat Rusmevichientong, Benjamin Van Roy: "Solitaire: Man VersusMachine". Advances in Neural Information Processing Systems 17 (NIPS 2004): 1553-1560
ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1112‫ؙٗ‬ٝ‫ٕךؙ؎ت‬٦ٕ‫ך‬㢌珏‫ؠ‬՛‫֭ؠ‬ᇥ೟֮փ֎֣֊ணև‫׊׋׈‬• ౅ష֭զᇸഊէӡጮ୶֌‫׈֊פ׸״׮‬ᅳ୶֌‫׮‬‫ࡤַפ׸״‬၌֚֔‫׊‬Ӣ֭఑ӣः቙֣֙ࡤ၌֚֔‫֊׊‬i• ࡴᄤ࿨֪֮ 1-3 ቙Æ ቎ଞ੄֦֮ 1 ቙֣֙• ౅ష֭զ֎֙֔‫׈‬փէӡᅳ୶֌‫בפ׸״׮‬ጮ୶֌֪኱֘Ӣ‫ב‬ኅฑ଺֪੔֘֊i• ฑ଺‫ב‬इև‫׊‬඘஽ӣ፯և֯ӣष෾ฑ଺‫ב‬ይև‫׊‬ӣ‫׮‬‫בחר‬ணፄ֖֥ଲ࿾ሑಠ֪֘‫׊‬ӣ့Æ ቎ଞ੄֦֮ኅฑ଺֪੔֘• ຎష֊‫׈‬඘షַ኱֘ࡤ၌‫ב‬੔֘֊iÆ ቎ଞ੄֦֮੔֘ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1113

2. ꟼ鸬灇瑔
‫ؙٗ‬ٝ‫ךؙ؎ت‬䧭⸆桦• Bjarnason ‫( ׈‬2007) [Bjarnason+07]• ؇‫ؚ‬՛‫༷פ׸׻׮؟‬ఫ‫ב‬ዿփ֞‫ءؚؔ׬‬՛‫့ׇ֥֢֪ب؜׬‬ӣ‫֭פי׵بآפ‬ถୱጴ‫ ב‬70 % ֊‫ ׈‬98.81% ֧෮࿊• ශ༭ (2018) [Shintani18]• 1000଼֭ഷৼვམ‫༷ב‬ఫӣถୱඡ໺֪ြ༥ׁ֖֭֞ 874ӣြ༥ᆊईႷ֧ᄕ࿊֦֌ׁ֭֞ 111ӣಐ৖โ‫ ׋‬15

• փ֙‫ׁ׋‬॰࿊‫ק‬՛ؕᄟ֭ถୱጴ‫ב‬૱్৿ಲଫ֪‫ׇ֢‬֥෮࿊֖֥փ‫׊‬[Bjarnason+07] Ronald Bjarnason, Prasad Tadepalli, Alan Fern: “Searching Solitaire in Real Time”.
Journal of the International Computer Games Association 30(3): pp.131-142 (2007)[Shintani 18] ශ༭ ᆈ᎙: “‫נ‬՛‫ק׾‬՛ؕզ‫פי׵بآפ‬է֭ถୱईႷต”, ༌80षගሇശጫॺव๺ே་व஬
࣏Ꭺᇌആ, 2018(1), pp.191-192 (2018-03-13)ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1114‫ؙٗ‬ٝ‫ךؙ؎ت‬鎘皾醱꧟ׁ• ࡴᄤँ‫[פי׵بآפ‬Longpre+09]• ‫נ‬՛‫֭׾‬቙෾‫ࡴב‬ᄤँ֘‫׊‬• ோӣ฾֭‫׮‬՛‫֭׽‬೟፬෾‫ܾ ׋֝׋֜ב‬, ‫׊֧֘ ݎ‬• ‫ בפب؞‬1, 2, 3, … , ݊ ֧֘‫׊‬• ‫נ‬՛‫֮׾‬๺ᆪ֦ (ܾ + ‫ ݊)ݎ‬቙• ඘ష֭౅֧֭֓቙෾֮႞࡝• ቎ଞ੄֦֮ӣ඘ష֭౅଼֭෾‫֥֖֧ ݉ ב‬,२ 1, 2, … , ݉ ቙֧ணև‫׊‬• එ֭ኴ༎‫ ב‬KLOND(ܾ, ‫ݎ‬, ݉) ֧ᅳ਋֘‫׊‬• ඘ష֭ვམ‫ב‬႞࡝ׁ֧֖֭֞‫ ב‬KLOND(ܾ, ‫֧ )ݎ‬ᅳ਋֘‫׊‬[Longpre+09] Luc Longpré and Pierre McKenzie: “The complexity of Solitaire”. Theoretical Computer Science, 410 (50),pp.5252-5260 (2009)ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1115‫ؙٗ‬ٝ‫ךؙ؎ت‬鎘皾醱꧟ׁ• ኴ༎‫ ב‬KLOND(ܾ, ‫ݎ‬, ݉) ֧ᅳ਋֘‫׊‬• ᅮമ࿨֩‫ ֮פי׵بآפ‬KLOND(2,2,7)

ܾ: ோ‫׮‬՛‫֭׽‬೟፬෾‫ݎ‬: ฾‫׮‬՛‫֭׽‬೟፬෾݉: ඘ష֭‫פ׸״׮‬෾݊: ‫פب؞‬෾• Longpré & McKenzie [Longpre+09] ֪‫֯׋ׇ‬ӣ• KLOND(b,r) ֮ NP-complete (֖֞֟ b, r ֮႞࡝֭࿊෾)• KLOND(2,1) ֮ NP-complete• KLOND(1,1) ֮ NL-hard• KLOND(1,0) ֮ AC0[Longpre+09] Luc Longpré and Pierre McKenzie: “The complexity of Solitaire”. Theoretical Computer Science, 410 (50),pp.5252-5260 (2009)ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1116

3. 灇瑔湡涸• ӡ௻೸࿨֪֮Ӣ‫֭פי׵بآפ‬ถୱጴ‫ב‬ਿ‫֞׀‬փ• ᅮമ࿨֩඘஽ӡ֘֩‫ ֠׎‬KLOND(2,2,7) ֊֣ n=13Ӣ֪֣փ֥ถୱጴ֭ભ໲࿨֩ཏ‫ב‬ነ‫֖֪֞֊׈‬փ• ֖֞֟ӣईႷ֩ഷৼვམ֭඘஽֭෾֋ሶ་֦ց‫֞׊‬‫׀‬ӣ༳റ֩૱్৿‫ءؚؔ׬‬՛‫֦֮ب؜׬‬ᆊई• ं֪ӣይև‫֞׋׈‬ഷৼვམ֋ถୱईႷ֊֨օ֊‫ ב‬10-9 ᅹ֦ᄕ࿊֦֌ׁ֧֖֥֞ 1051 Ⴉ֊֊‫׊‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1117灇瑔湡涸• ༳റ֩૱్৿‫ءؚؔ׬‬՛‫֦֮ب؜׬‬ᆊई• ணև‫׊׋׈‬ሑሓ Æ ጫᎪ࿨֩शื• ഷৼვམ֭ᇀ፬֧෾ևඑ֑• ቎ಱ࿨֪၍ཏ֩ഷৼვམ• ነ‫֪֊׈‬श֐‫׊‬श֐֩փഷৼვམ• ց‫׊‬೟֭ඡ໺֪਀ཧ֦֌‫׊‬ഷৼვམ• փֽ֧֭֒‫୲׌‬ऐ࿨֩‫֋ח׼יח‬ՔՔՔ• ૱్৿ಲଫ‫֞֗ྫྷב‬৑ళ֪‫ׇ֥֢‬ӣตಱ‫ֿ֧֒֊֣ב‬֦֮֌֩փ֊i勓煝疴‫ס‬潨溷• ࡴᄤँ‫֭פי׵بآפ‬օ֠ӣ؆‫ؖ؞‬՛‫֭״‬ཏ֋൚֔֩ᄧࡗ֪֣փ֥૱్৿ಲଫ‫ב‬பփถୱጴ‫ב‬ਿ‫׊׀‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1118

4.䲿周䩛岀

ܾ: ோ‫׮‬՛‫֭׽‬೟፬෾‫ݎ‬: ฾‫׮‬՛‫֭׽‬೟፬෾݉: ඘ష֭‫פ׸״׮‬෾݊: ‫פب؞‬෾杅媗曫‫ؠ‬ٞ٤‫סؠؕر‬㴻聋• KLOND(b,r,m,n)• ‫פب؞‬෾ n ‫ିב‬࿊֘‫׊‬• ඘ష֭२‫ ֮פ׸״׮‬1, 2, …, m ቙• ౅ష֮

௠(௠ାଵ)
ܾ+‫݊ ݎ‬െ቙ଶ‫ر‬3ՔՔՔ‫ر‬n‫د‬1‫د‬2‫د‬3ՔՔՔ

‫د‬n‫ح‬1‫ح‬2‫ح‬3ՔՔՔ‫ح‬n‫س‬1‫س‬2‫س‬3ՔՔՔ‫س‬nr=2b=2ՔՔՔヅヅヅ‫ر‬2ヅヅヅ‫ر‬1mnຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-11

19䲿周䩛岀㵅닫• ኬ࿨• ༷ఫ֪ጅ֘‫׊‬ಐ৖‫׊ָྔב‬• ሑሓ1. ‫֪ؕ׵ب؞‬ഷৼვམ‫ב‬ภถ֘‫׊‬
2. ༷ఫ‫ׇ֥֢֪֭֜ؕׯ؟שؠח‬ኴ༎‫ב‬श֎• ༷ఫ֮ A* ‫בؕׯ؟שؠח‬ዿփ‫׊‬• ภถ֖֞ඡ໺֋ࡴ࿊෾ (100ቮ) ‫ྖב‬և‫༷֧׊‬ఫ‫ב‬໫֠โ‫׊‬• එ਋ 1-2 ‫׉ૅב‬ᇪ֖ (1000ष) ಲப֘‫׊‬• ଅऐ֮զถୱईႷէզถୱᆊႷէֽ֮֞զ‫׽כחؕי״‬է• ภถ֖֞ඡ໺଼֭෾‫ב‬਋Ꭹ֘‫׊‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1120䲿周䩛岀㵅닫• ኬ࿨• ถୱጴ‫ב‬෮࿊֘‫׊‬• ሑሓ1. ‫֪ؕ׵ب؞‬ഷৼვམ‫ב‬ภถ֘‫׊‬
2. ༷ఫ‫ׇ֥֢֪֭֜ؕׯ؟שؠח‬ኴ༎‫ב‬श֎• ༷ఫ֮ A* ‫בؕׯ؟שؠח‬ዿփ‫׊‬• ภถ֖֞ඡ໺֋ࡴ࿊෾ (10ቮ) ‫ྖב‬և‫༷֧׊‬ఫ‫ב‬໫֠โ‫׊‬• එ਋ 1-2 ‫׉ૅב‬ᇪ֖ (1000ष) ಲப֘‫׊‬• ଅऐ֮զถୱईႷէզถୱᆊႷէֽ֮֞զ‫׽כחؕי״‬էຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1121

5. 㹋꿀穠卓‫ה‬罋㻊

KLOND(ܾ, ‫ݎ‬, ݉, ݊)ܾ: ோ‫׮‬՛‫֭׽‬೟፬෾‫ݎ‬: ฾‫׮‬՛‫֭׽‬೟፬෾݉: ඘ష֭‫פ׸״׮‬෾݊: ‫פب؞‬෾㵅닫‫ס‬篙卸• ༷ఫᄧࡗ֭॰ጴᇀᆑ: KLOND(2,2,7,13)80%፫ูถୱጴӡ‫׭بءן‬න֭ๆ‫׋‬๦‫؞ץ‬؊Ӣ༷ఫถୱ֖֞ष෾
ӡ1000ष
֭օ֠Ӣ
50ቮ

100ቮ

0༷ఫ֖֞ඡ໺෾

ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1122㹋꿀穠卓‫ה‬罋㻊㵅닫‫ס‬篙卸籽‫׀‬• ༷ఫᄧࡗ֋൚֔փ඘஽֪֣փ֥४་֖֥‫֧׊־‬ӣ55%༷ఫถୱ֖֞ष෾
ӡ1000ष
֭օ֠Ӣ
05,00010,000༷ఫ֖֞ඡ໺෾ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1123㹋꿀穠卓‫ה‬罋㻊㵅닫‫ס‬脝㷋• ༷ఫᄧࡗӡඡ໺෾Ӣ‫ ב‬100ቮ֪଺࿊֘‫֧׊‬ӣ๺໲֭ዃ80% ‫נב‬؅՛֦֌‫׊‬• ༷ఫᄧࡗӡඡ໺෾Ӣ‫ ב‬1ቮ֪଺࿊ׁ֖֥ӣ๺໲֭ዃ55% ‫נב‬؅՛֦֌‫׊‬• ᇀᆑ֭௻ᆇཏ֮֊֩‫׉‬൚֔փ• 1,000 ֣֙ᄧࡗ‫ב‬તโ‫֧׊‬ӣ 1,001-2,000 ց֞‫׉‬• 10,000 ֣֙ᄧࡗ‫ב‬તโ‫֧׊‬ӣ 1-10,000 ց֞‫׉‬• ॰ጴ࿨֪෮࿊֘‫֦֐֟׊‬ց‫֯׋‬ӣ֜‫ֺ֨׋‬ෆփ༷ఫ‫ב‬பօᅢጅ֮֩փຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1124

KLOND(ܾ, ‫ݎ‬, ݉, ݊)㹋꿀穠卓‫ה‬罋㻊ܾ: ோ‫׮‬՛‫֭׽‬೟፬෾‫ݎ‬: ฾‫׮‬՛‫֭׽‬೟፬෾݉: ඘ష֭‫פ׸״׮‬෾݊: ‫פب؞‬෾篙卸 ր䧯Ⲍ㎇俙雧鉿㎇俙ց• ቎጖ਿ‫֞׀‬փզถୱጴէ֦֮֩փ֧֪֒཯࡝
n=3n=4n=5n=7n=9n=11n=13ถୱ֖֞ष෾ಀபष෾

100%80%60%40%20%0%123456
඘ష֭౅֭෾ mຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-117825

㹋꿀穠卓‫ה‬罋㻊‫֭׽כחؕי״‬෾ಀபष෾• ༷ఫ‫ב‬ထཨ֦໫֠โ֢֥փ‫׊‬• ถୱጴ֮࿃֎ଣׁู‫֥׋׈‬փ‫׊‬ईႷต֋ஸփ
n=7n=9n=11n=13

100%
80%
60%
40%
20%0%
1234567඘ష֭౅֭෾ mຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-118926

㹋꿀穠卓‫ה‬罋㻊፯Ӣ
• 1000 ଼֭ഷৼვམ‫ב‬ภถ֖֧֞֌ӣ• ถୱईႷ֧ᇀ֊ׁ֢֭֞ 500 ଼ (=A)• ถୱᆊႷ֧ᇀ֊ׁ֢֭֞ 300 ଼ (=B)• ‫ ׽כחؕי״‬200 ଼ (=C)

• (ถୱष෾ A) / (ಀபष෾ A+B+C) = 500/1000 = 50%• (ถୱष෾ A) / (‫׽כחؕי״‬ൊ֎ಀபष෾ A+B) = 500/800 = 62.5%• ׁ֖‫֖֞׽כחؕי״‬ഷৼვམ֭ᇀᆑ֧‫֢֞֊֖֩׽כחؕי״‬ഷৼვམ֭ᇀᆑ֋ಉ֥փ‫ं֧׊‬࿊֘‫֧׊‬ଢ଼ೄ֪‫ׇ֥֢‬቎጖֭ถୱጴ֋෮࿊֦֌‫׊‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1127㹋꿀穠卓‫ה‬罋㻊ถୱ֖֞ष෾‫֖׽כחؕי״‬֩֊֢֞ಀபष෾• զถୱ֖֞ष෾‫֢֞֊֖֩׽כחؕי״‬ಀபष෾է
n=3n=4n=5n=7n=9n=11
n=13

1
0.8
0.6
0.4
0.2
01

2

3456
඘ష֭౅֭෾ mຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-117828

6. ‫➙ה׭הת‬䖓‫ך‬铬겗‫״כױ‬• ‫֭פי׵بآפ‬ถୱጴ‫ב‬ਿ‫֪׀֞׊׀‬ӣၟ೜ᄟ֭ถୱ
ጴӡ֭෮࿊ཏӢ‫ב‬૱్৿ಲଫ֪‫ׇ֥֢‬ਿ‫֞׀‬• ଯቹ֩ཏ֮ቴशଂՔՔՔ♀䔿‫ס‬鞏꾴• ‫׮‬՛‫֭׽‬೟፬‫଺ב‬࿊֖֞඘஽֪֣փ֥ถୱጴ‫ב‬ਿ‫׀‬‫׊‬ӡ૱్৿ಲଫ֪‫ׇ֥֢‬Ӣ• KLOND-FLAT(1,1) ֭૱్ፘ‫ב‬ਿ‫׊׀‬• KLOND-FLAT ֮ഷৼඡ໺֪։փ֥౅ష֋઱֦ց‫ׁ֭׊‬ຎ஽֚‫ק‬՛ؕ؆‫ؠׯ‬،‫׽פל׭آ‬༌14षଞ੄ആव (ࣝ:ဃྫྷ་) 2019.3.10-1129