數獨的解法與技巧？

數獨是源于18世紀瑞士的一種數學游戲。是一種運用紙、筆進行演算的邏輯游戲。玩家需要根據9*9盤面上的數字推理出所有剩余的空格數字，并滿足每一行、每一列、每一個粗線宮（3*3）內的數字均含1-9，不重復。

數獨的規則

在空格內填入數字1-9，使得每行、每列和每個宮格內數字都不重復。

注意：數獨題目滿足條件的答案是唯一的。

數獨的元素

數獨基本元素示意圖單元格：數獨中最小的單元，標準數獨中共有81個；

行：橫向9個單元格的集合；

列：縱向9個單元格的集合；

宮：粗黑線劃分的區域，標準數獨中為3×3的9個單元格的集合；

已知數：數獨初始盤面給出的數字；

候選數：每個空單元格中可以填入的數字。

數獨技巧

宮內排除法

排除法就是利用數獨中行、列和宮內不能填入相同數字的規則，利用已出現的數字對同 行、同列和同官內其他格逬行排位相同數字的方法。

宮內排除法就是將一個宮作為目標，用某個數字對它進行排除，最終得到這個宮內只有一 格出現該數字的方法。技巧示意圖：

如上圖所示，A2、B4和F7三格內的1都對三宮進行排除，這時三宮內只有C9格可以填入 1，本圖例就是對三宮運用的排除法。

行列排除法

行列排除法就是將一行或一列作為目標，用某個數字對它進行排除，最終得到這個行列內 只有一格出現該數字的方法。技巧示意圖：

如上圖所示，D2和B8兩格內的6都對F行進行排除，這時F行內只有F5格可以填入6，本圖 例就是對F行運用的排除法。

區塊排除法

區塊排除法就是先用宮內排除法在某個宮內形成一個區塊，利用該區塊的排除再結合其他已知數共同確定某宮內只有一格出現該數字的方法。技巧示意圖：

如上圖所示，B4格的7對五宮進行排除，在五宮內形成了一個含數字7的區塊。無論該區 塊中F5格是7還是F6格是7，都可以對F行其他格的7進行排除。再結合H7格的7同時對六宮進 行排除，得到六宮內只有D8格可以填7。

宮內數對占位法

數對占位法指的是在某個區域中使得某兩數只能出現在某兩格內，這時雖然無法判斷這兩個數字的位置，但可以利用兩數的占位排斥掉其他數字出現在這兩格，再結合排除法就可以間 接填出下個數字。技巧示意圖：

宮內數對占位法

如圖所示，利用D行和7列中的已知數3、5對六宮排除，得到在E8和F8兩格形成了一個數對，該數對排斥其他數字填入這兩格。這時再利用D4和F1兩格中的7對六宮進行排除，得到六宮中只有E7格可以填入7。

唯余解法

唯余法就是利用數獨中每格內都只有9種數字的可能性，如果某格中有8種數字都不能填，只能填入唯一未出現數字的方法。技巧示意圖：

唯余解法

如上圖所示，C行有已知數1、2 ，三宮有已知數3、4、5 ，9列有已知數5、6、7、8 ，上述8種不同的數字，同時對C9格產生影響，使得C9格不能填入這8種數字，得到C9格內只能填入數字9，否則就出現同行、同列或同宮中數字相同的情況。

行列區塊法

行列區塊法指的是利用行列排除，在某行或列內制造出一個區塊，利用該區塊對該區塊所在宮的其他格進行刪除的方法。技巧示意圖：

行列區塊發

如上圖所示，A9和12兩格的1對5列進行排除，使得5列的1只能在D5、E5和F5三格之中，這時在5列內制造了一個含5的區塊，該區塊同時也存在于五直中，所以可以排除掉五宮其它格中的1。這時再結合D行和6列的已知數字，可以唯余得到D6格內只能填入9 。

行列內數對占位法

數對占位法，在上面的宮內數對占位法中，我們已經學過數又寸占位法，這里講的是數對出現行列里的情況，這時的觀察難度會大大增加，本技巧也屬于難度較大的技巧之一。技巧示意 圖：

如圖所示，利用四宮和8列的已知數2、7，同時對F行進行排除，在F有得到數字2、7只能填在F6和F9兩格內，這時在F行的這兩格內形成2、7數對。再觀察A7和H8兩格的8對六宮的排除，六宮內只有E9格內可以填入8。

好了，如果你已經熟練掌握了上規則和技巧，就可以小試身手啦！

%3Chowto_content%3E[{"type":"paragraph","attrs":{"is_abstract":true},"children":[{"type":"text","text":"數獨是源于18世紀瑞士的一種數學游戲。是一種運用紙、筆進行演算的邏輯游戲。玩家需要根據9*9盤面上的數字推理出所有剩余的空格數字，并滿足每一行、每一列、每一個粗線宮（3*3）內的數字均含1-9，不重復。","id":""}],"text":"","id":"doxcnQeQiWMe0QMYaWMZCpSJOCb"},{"type":"heading","attrs":{"level":1},"children":[{"type":"text","text":"數獨的規則","id":""}],"text":"","id":"doxcnkuoSkwCIK8wqAbgpljAN3b"},{"type":"paragraph","children":[{"type":"text","text":"在空格內填入數字1-9，使得每行、每列和每個宮格內數字都不重復。","id":""}],"text":"","id":"doxcnYa0sSMGGGouECsaXE91P5g"},{"type":"paragraph","children":[{"type":"text","text":"注意：數獨題目滿足條件的答案是唯一的。","id":""}],"text":"","id":"doxcnwcsa6myGO0AcSutsWVfoif"},{"type":"heading","attrs":{"level":1},"children":[{"type":"text","text":"數獨的元素","id":""}],"text":"","id":"doxcnc0Q0uyGEwsM42VYwfnFFlh"},{"type":"paragraph","children":[{"type":"text","text":"數獨基本元素示意圖","id":""},{"type":"external_link","attrs":{"url":"https%3A%2F%2Fbaike.so.com%2Fdoc%2F6733917-6948278.html"},"children":[{"type":"text","text":"單元格","id":""}],"text":"","id":""},{"type":"text","text":"：數獨中最小的單元，標準數獨中共有81個；","id":""}],"text":"","id":"doxcnqu6eyAmecgiUKYQ1zxWozf"},{"type":"paragraph","children":[{"type":"text","text":"行：橫向9個單元格的集合；","id":""}],"text":"","id":"doxcnumwQEwCC2CIUMLFwHQ1Gib"},{"type":"paragraph","children":[{"type":"text","text":"列：縱向9個單元格的集合；","id":""}],"text":"","id":"doxcnU6K8akqMca4WG6diQkjZyc"},{"type":"paragraph","children":[{"type":"text","text":"宮：粗黑線劃分的區域，標準數獨中為3×3的9個單元格的集合；","id":""}],"text":"","id":"doxcnm6YeYoEkIuY0DlhJZCTYIS"},{"type":"paragraph","children":[{"type":"text","text":"已知數：數獨初始盤面給出的數字；","id":""}],"text":"","id":"doxcnA0cQkmWaUsYAmXVt4tsV6y"},{"type":"paragraph","children":[{"type":"external_link","attrs":{"url":"https%3A%2F%2Fbaike.so.com%2Fdoc%2F369394-391302.html"},"children":[{"type":"text","text":"候選","id":""}],"text":"","id":""},{"type":"text","text":"數：每個空單元格中可以填入的數字。","id":""}],"text":"","id":"doxcneGmk8mOKKysIkjcIk9QZie"},{"type":"image","attrs":{"height":460,"note":[{"type":"text","text":"數獨的元素","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/af9fdfe172a84efcb55ccb8f43d1f513","width":545},"text":"","id":"doxcnkI6m0eSaY4i6geSwEV6sZF"},{"type":"heading","attrs":{"level":1},"children":[{"type":"text","text":"數獨技巧","id":""}],"text":"","id":"doxcnUSeMU0UOOUKY4z77SraWQj"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"宮內排除法","id":""}],"text":"","id":"doxcn2y80ECwiIuA2kPsl94Ncud"},{"type":"paragraph","children":[{"type":"text","text":"排除法就是利用數獨中行、列和宮內不能填入相同數字的規則，利用已出現的數字對同 行、同列和同官內其他格逬行排位相同數字的方法。","id":""}],"text":"","id":"doxcnoweqYycoG8qaEHJzid40mg"},{"type":"paragraph","children":[{"type":"text","text":"宮內排除法就是將一個宮作為目標，用某個數字對它進行排除，最終得到這個宮內只有一 格出現該數字的方法。技巧示意圖：","id":""}],"text":"","id":"doxcnKEEy8E2WwOc2MffE6jSTNf"},{"type":"image","attrs":{"height":449,"note":[{"type":"text","text":"宮內排除法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/cf689b8ab611404f8744c4af4606c406","width":431},"text":"","id":"doxcn6m8UCgQIMIEEmKXLr8aObd"},{"type":"paragraph","children":[{"type":"text","text":"如上圖所示，A2、B4和F7三格內的1都對三宮進行排除，這時三宮內只有C9格可以填入 1，本圖例就是對三宮運用的排除法。","id":""}],"text":"","id":"doxcniUu2cIUqSYEyyKPHuzW2xb"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列排除法","id":""}],"text":"","id":"doxcny0cscY4GKgcKcrOYskzYqh"},{"type":"paragraph","children":[{"type":"text","text":"行列排除法就是將一行或一列作為目標，用某個數字對它進行排除，最終得到這個行列內 只有一格出現該數字的方法。技巧示意圖：","id":""}],"text":"","id":"doxcnamqmeQ64eoOai0GsJ0nKXb"},{"type":"image","attrs":{"height":466,"note":[{"type":"text","text":"行列排除法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/92b3b5ce45be4191ad1ffec82c6488b1","width":439},"text":"","id":"doxcnWcqSUyOyg0UKWQ1CEtCVKh"},{"type":"paragraph","children":[{"type":"text","text":"如上圖所示，D2和B8兩格內的6都對F行進行排除","id":""},{"type":"text","text":"，這時F行內只有F5格可以填入6，","id":""},{"type":"text","text":"本圖 例就是對F行運用的排除法。","id":""}],"text":"","id":"doxcnwKAk0AKuOWwSsxFAmgMqXf"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"區塊排除法","id":""}],"text":"","id":"doxcniAce6euUk8q6EpMTfgzYLh"},{"type":"paragraph","children":[{"type":"text","text":"區塊排除法就是","id":""},{"type":"text","text":"先用宮","id":""},{"type":"text","text":"內排除法在某個宮內形成一個區塊，利用該區塊的排除再結合","id":""},{"type":"text","text":"其他","id":""},{"type":"text","text":"已知數共同確定某宮內只有一格出現該數字的方法。技巧示意圖：","id":""}],"text":"","id":"doxcnwae4ucuEsQ24AdX1Lphjig"},{"type":"image","attrs":{"height":451,"note":[{"type":"text","text":"區塊排除法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/16d8b27fd898423999d142d6795c525a","width":432},"text":"","id":"doxcn6SGkIuuaUAoQQhJsi1EHfd"},{"type":"paragraph","children":[{"type":"text","text":"如上圖所示，B4格的7對五宮進行排除，在五宮內形成了一個含數字7的區塊。無論該區 塊中F5格是7還是F6格是7，都可以對F行其他格的7進行排除。再結合H7格的7同時對六宮進 行排除，得到六宮內只有D8格可以填7。","id":""}],"text":"","id":"doxcneqKaq2yE6c6AiIlofNjezd"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"宮內數對占位法","id":""}],"text":"","id":"doxcnu4kGCe0IigOMk1cNKknR2d"},{"type":"paragraph","children":[{"type":"text","text":"數對占位法指的是在某個區域中使得某兩數只能出現在某兩格內，這時雖然無法判斷這兩個數字的位置，但可以利用兩數的占位排斥掉其他數字出現在這兩格，再結合排除法就可以間 接填出下個數字。技巧示意圖：","id":""}],"text":"","id":"doxcn2ayg40kg8UuSYLgpR9AdGd"},{"type":"paragraph","children":[{"type":"text","text":" ","id":""}],"text":"","id":"doxcnkgoo0w2IgGcGYzW8Rubjvb"},{"type":"image","attrs":{"height":400,"note":[{"type":"text","text":"宮內數對占位法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/24978a6654f84380b0a52e90bb7f912b","width":472},"text":"","id":"doxcnkwiOgeWSKmk8Y3RCRBV17c"},{"type":"paragraph","children":[{"type":"text","text":" 宮內數對占位法","id":""}],"text":"","id":"doxcncSWgoQMkKsKeqYyHGc0gRb"},{"type":"paragraph","children":[{"type":"text","text":"如圖所示，利用D行和7列中的已知數3、5對六宮排除，得到在E8和F8兩格形成了一個數對，該數對排斥其他數字填入這兩格。這時再利用D4和F1兩格中的7對六宮進行排除，得到六宮中只有E7格可以填入7。","id":""}],"text":"","id":"doxcn4WAscWIAmQc8QBfp3PLoJc"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"唯余解法","id":""}],"text":"","id":"doxcnq0kUyOce4IquIJvfeMSmZd"},{"type":"paragraph","children":[{"type":"text","text":"唯余法就是利用數獨中每格內都只有9種數字的可能性，如果某格中有8種數字都不能填，只能填入唯一未出現數字的方法。技巧示意圖：","id":""}],"text":"","id":"doxcneQeOI28E2awqKwqYShqSof"},{"type":"paragraph","children":[{"type":"text","text":" ","id":""}],"text":"","id":"doxcnA6eeMMsYEsAoM199oeavAc"},{"type":"image","attrs":{"height":348,"note":[{"type":"text","text":"唯余解法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/9280db48a8d546af9a904880f5b055d4","width":407},"text":"","id":"doxcnqE08K8I4sCGUkz8EAwCW0N"},{"type":"paragraph","children":[{"type":"text","text":" 唯余解法","id":""}],"text":"","id":"doxcn68o0soY0QG0smgu75VY3uc"},{"type":"paragraph","children":[{"type":"text","text":"如上圖所示，C行有已知數1、","id":""},{"type":"text","text":"2 ，三","id":""},{"type":"text","text":"宮有已知數3、4、5 ，9列有已知數5、6、7、8 ，上述8種不同的數字，同時對C9格產生影響，使得C9格不能填入這8種數字，得到C9格內只能填入數字9，否則就出現同行、同列或同宮中數字相同的情況。","id":""}],"text":"","id":"doxcnioEc0UGQ6UIeeoE4anndIh"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列區塊法","id":""}],"text":"","id":"doxcngOKiCumGmssEK45PeH2Ekg"},{"type":"paragraph","children":[{"type":"text","text":"行列區塊法指的是利用行列排除，在某行或列內制造出一個區塊，利用該區塊對該區塊所在宮的其他格進行刪除的方法。技巧示意圖：","id":""}],"text":"","id":"doxcnQ44KSsA2o6KI4lKyQ1h17t"},{"type":"image","attrs":{"height":415,"note":[{"type":"text","text":"行列區塊法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/efd0b04aed6b4838b29c8163733ab663","width":439},"text":"","id":"doxcnO6cWgicy88SucLGXwyCkBf"},{"type":"paragraph","children":[{"type":"text","text":" 行列區塊發","id":""}],"text":"","id":"doxcnWGCeu4G400KaIZnEwbMxLd"},{"type":"paragraph","children":[{"type":"text","text":"如上圖所示，A9和12兩格的1對5列進行排除，使得5列的1只能在D5、E5和F5三格之中，這時在5列內制造了一個含5的區塊，該區塊同時也存在于五直中，所以可以排除掉五宮其它格中的1。這時再結合D行和6列的已知數字，可以唯余得到D6格內只能填入9 。","id":""}],"text":"","id":"doxcneYeSCYiCg6GiKCyjUtyyHb"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列內數對占位法","id":""}],"text":"","id":"doxcnEYs2AkacMCqW0qLhW9j3fk"},{"type":"paragraph","children":[{"type":"text","text":"數對占位法，在上面的宮內數對占位法中，我們已經學過數又寸占位法，這里講的是數對出現行列里的情況，這時的觀察難度會大大增加，本技巧也屬于難度較大的技巧之一。技巧示意 圖： ","id":""}],"text":"","id":"doxcnSKw48WeA2Ek4iGuRixfUah"},{"type":"image","attrs":{"height":422,"note":[{"type":"text","text":"行列內數對占位法","id":""}],"url":"{{image_domain}}tos-cn-i-qvj2lq49k0/26b33320ed6545db8894d5f904a26e67","width":396},"text":"","id":"doxcnscC4IaKggeEYgpanK2M2lh"},{"type":"paragraph","children":[{"type":"text","text":"如圖所示，利用四宮和8列的已知數2、7，同時對F行進行排除，在F有得到數字2、7只能填在F6和F9兩格內，這時在F行的這兩格內形成2、7數對。再觀察A7和H8兩格的8對六宮的排除","id":""},{"type":"text","text":"，","id":""},{"type":"text","text":"六宮內只有E9格內可以填入8。","id":""}],"text":"","id":"doxcnkaM4uwISa26EAHkC3HVHGd"},{"type":"paragraph","children":[{"type":"text","text":"好了，如果你已經熟練掌握了上規則和技巧，就可以小試身手啦！","id":""}],"text":"","id":"doxcns4w02IGMGAiG4sxIPTuwob"},{"type":"paragraph","children":[{"type":"text","text":"","id":""}],"text":"","id":"doxcnOWME4GiyiWWQT0A5wtXBgf"}]%3C%2Fhowto_content%3E