數(shù)獨的解法與技巧？

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

數(shù)獨的規(guī)則

在空格內(nèi)填入數(shù)字1-9，使得每行、每列和每個宮格內(nèi)數(shù)字都不重復(fù)。

注意：數(shù)獨題目滿足條件的答案是唯一的。

數(shù)獨的元素

數(shù)獨基本元素示意圖單元格：數(shù)獨中最小的單元，標準數(shù)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(qū)域，標準數(shù)獨中為3×3的9個單元格的集合；

已知數(shù)：數(shù)獨初始盤面給出的數(shù)字；

候選數(shù)：每個空單元格中可以填入的數(shù)字。

數(shù)獨技巧

宮內(nèi)排除法

排除法就是利用數(shù)獨中行、列和宮內(nèi)不能填入相同數(shù)字的規(guī)則，利用已出現(xiàn)的數(shù)字對同 行、同列和同官內(nèi)其他格逬行排位相同數(shù)字的方法。

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

如上圖所示，A2、B4和F7三格內(nèi)的1都對三宮進行排除，這時三宮內(nèi)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(shù)字對它進行排除，最終得到這個行列內(nèi) 只有一格出現(xiàn)該數(shù)字的方法。技巧示意圖：

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

區(qū)塊排除法

區(qū)塊排除法就是先用宮內(nèi)排除法在某個宮內(nèi)形成一個區(qū)塊，利用該區(qū)塊的排除再結(jié)合其他已知數(shù)共同確定某宮內(nèi)只有一格出現(xiàn)該數(shù)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(nèi)形成了一個含數(shù)字7的區(qū)塊。無論該區(qū) 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(jié)合H7格的7同時對六宮進 行排除，得到六宮內(nèi)只有D8格可以填7。

宮內(nèi)數(shù)對占位法

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

宮內(nèi)數(shù)對占位法

如圖所示，利用D行和7列中的已知數(shù)3、5對六宮排除，得到在E8和F8兩格形成了一個數(shù)對，該數(shù)對排斥其他數(shù)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(shù)獨中每格內(nèi)都只有9種數(shù)字的可能性，如果某格中有8種數(shù)字都不能填，只能填入唯一未出現(xiàn)數(shù)字的方法。技巧示意圖：

唯余解法

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

行列區(qū)塊法

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

行列區(qū)塊發(fā)

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(nèi)制造了一個含5的區(qū)塊，該區(qū)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(jié)合D行和6列的已知數(shù)字，可以唯余得到D6格內(nèi)只能填入9 。

行列內(nèi)數(shù)對占位法

數(shù)對占位法，在上面的宮內(nèi)數(shù)對占位法中，我們已經(jīng)學(xué)過數(shù)又寸占位法，這里講的是數(shù)對出現(xiàn)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(shù)2、7，同時對F行進行排除，在F有得到數(shù)字2、7只能填在F6和F9兩格內(nèi)，這時在F行的這兩格內(nèi)形成2、7數(shù)對。再觀察A7和H8兩格的8對六宮的排除，六宮內(nèi)只有E9格內(nèi)可以填入8。

好了，如果你已經(jīng)熟練掌握了上規(guī)則和技巧，就可以小試身手啦！

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只有一格出現(xiàn)該數(shù)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(nèi)的6都對F行進行排除","id":""},{"type":"text","text":"，這時F行內(nèi)只有F5格可以填入6，","id":""},{"type":"text","text":"本圖 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宮內(nèi)數(shù)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(shù)3、5對六宮排除，得到在E8和F8兩格形成了一個數(shù)對，該數(shù)對排斥其他數(shù)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(shù)獨中每格內(nèi)都只有9種數(shù)字的可能性，如果某格中有8種數(shù)字都不能填，只能填入唯一未出現(xiàn)數(shù)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(shù)1、","id":""},{"type":"text","text":"2 ，三","id":""},{"type":"text","text":"宮有已知數(shù)3、4、5 ，9列有已知數(shù)5、6、7、8 ，上述8種不同的數(shù)字，同時對C9格產(chǎn)生影響，使得C9格不能填入這8種數(shù)字，得到C9格內(nèi)只能填入數(shù)字9，否則就出現(xiàn)同行、同列或同宮中數(shù)字相同的情況。","id":""}],"text":"","id":"doxcnioEc0UGQ6UIeeoE4anndIh"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列區(qū)塊法","id":""}],"text":"","id":"doxcngOKiCumGmssEK45PeH2Ekg"},{"type":"paragraph","children":[{"type":"text","text":"行列區(qū)塊法指的是利用行列排除，在某行或列內(nèi)制造出一個區(qū)塊，利用該區(qū)塊對該區(qū)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(qū)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(qū)塊發(fā)","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(nèi)制造了一個含5的區(qū)塊，該區(qū)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(jié)合D行和6列的已知數(shù)字，可以唯余得到D6格內(nèi)只能填入9 。","id":""}],"text":"","id":"doxcneYeSCYiCg6GiKCyjUtyyHb"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列內(nèi)數(shù)對占位法","id":""}],"text":"","id":"doxcnEYs2AkacMCqW0qLhW9j3fk"},{"type":"paragraph","children":[{"type":"text","text":"數(shù)對占位法，在上面的宮內(nèi)數(shù)對占位法中，我們已經(jīng)學(xué)過數(shù)又寸占位法，這里講的是數(shù)對出現(xiàn)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(nèi)數(shù)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(shù)2、7，同時對F行進行排除，在F有得到數(shù)字2、7只能填在F6和F9兩格內(nèi)，這時在F行的這兩格內(nèi)形成2、7數(shù)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(nèi)只有E9格內(nèi)可以填入8。","id":""}],"text":"","id":"doxcnkaM4uwISa26EAHkC3HVHGd"},{"type":"paragraph","children":[{"type":"text","text":"好了，如果你已經(jīng)熟練掌握了上規(guī)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