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数独的解法与技巧

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数独的解法与技巧

数独是源于18世纪瑞士的一种数学游戏。是一种运用纸、笔进行演算的逻辑游戏。玩家需要根据9*9盘面上的数字推理出所有剩余的空格数字,并满足每一行、每一列、每一个粗线宫(3*3)内的数字均含1-9,不重复。

数独的规则

在空格内填入数字1-9,使得每行、每列和每个宫格内数字都不重复。

注意:数独题目满足条件的答案是唯一的。

数独的元素

数独基本元素示意图单元格:数独中最小的单元,标准数独中共有81个

行:横向9个单元格的集合

列:纵向9个单元格的集合

宫:粗黑线划分的区域,标准数独中为3×3的9个单元格的集合

已知数:数独初始盘面给出的数字

候选数:每个空单元格中可以填入的数字。

数独技巧

宫内排除法

排除法就是利用数独中行、列和宫内不能填入相同数字的规则,利用已出现的数字对同 行、同列和同官内其他格逬行排位相同数字的方法。

宫内排除法就是将一个宫作为目标,用某个数字对它进行排除,最终得到这个宫内只有一 格出现该数字的方法。技巧示意图:

如上图所示,A2、B4和F7三格内的1都对三宫进行排除,这时三宫内只有C9格可以填入 1,本图例就是对三宫运用的排除法。

行列排除法

行列排除法就是将一行或一列作为目标,用某个数字对它进行排除,最终得到这个行列内 只有一格出现该数字的方法。技巧示意图:

如上图所示,D2和B8两格内的6都对F行进行排除,这时F行内只有F5格可以填入6,本图 例就是对F行运用的排除法。

区块排除法

区块排除法就是先用宫内排除法在某个宫内形成一个区块,利用该区块的排除再结合其他已知数共同确定某宫内只有一格出现该数字的方法。技巧示意图:

如上图所示,B4格的7对五宫进行排除,在五宫内形成了一个含数字7的区块。无论该区 块中F5格是7还是F6格是7,都可以对F行其他格的7进行排除。再结合H7格的7同时对六宫进 行排除,得到六宮内只有D8格可以填7。

宫内数对占位法

数对占位法指的是在某个区域中使得某两数只能出现在某两格内,这时虽然无法判断这两个数字的位置,但可以利用两数的占位排斥掉其他数字出现在这两格,再结合排除法就可以间 接填出下个数字。技巧示意图:

宫内数对占位法

如图所示,利用D行和7列中的已知数3、5对六宫排除,得到在E8和F8两格形成了一个数对,该数对排斥其他数字填入这两格。这时再利用D4和F1两格中的7对六宫进行排除,得到六宫中只有E7格可以填入7。

唯余解法

唯余法就是利用数独中每格内都只有9种数字的可能性,如果某格中有8种数字都不能填,只能填入唯一未出现数字的方法。技巧示意图:

唯余解法

如上图所示,C行有已知数1、2 ,三宫有已知数3、4、5 ,9列有已知数5、6、7、8 ,上述8种不同的数字,同时对C9格产生影响,使得C9格不能填入这8种数字,得到C9格内只能填入数字9,否则就出现同行、同列或同宫中数字相同的情况。

行列区块法

行列区块法指的是利用行列排除,在某行或列内制造出一个区块,利用该区块对该区块所在宫的其他格进行删除的方法。技巧示意图:

行列区块发

如上图所示,A9和12两格的1对5列进行排除,使得5列的1只能在D5、E5和F5三格之中,这时在5列内制造了一个含5的区块,该区块同时也存在于五直中,所以可以排除掉五宫其它格中的1。这时再结合D行和6列的已知数字,可以唯余得到D6格内只能填入9 。

行列内数对占位法

数对占位法,在上面的宫内数对占位法中,我们已经学过数又寸占位法,这里讲的是数对出现行列里的情况,这时的观察难度会大大增加,本技巧也属于难度较大的技巧之一。技巧示意 图:

如图所示,利用四宫和8列的已知数2、7,同时对F行进行排除,在F有得到数字2、7只能填在F6和F9两格内,这时在F行的这两格内形成2、7数对。再观察A7和H8两格的8对六宫的排除,六宫内只有E9格内可以填入8。

好了,如果你已经熟练掌握了上规则和技巧,就可以小试身手啦!

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宫内数对占位法","id":""}],"text":"","id":"doxcncSWgoQMkKsKeqYyHGc0gRb"},{"type":"paragraph","children":[{"type":"text","text":"如图所示,利用D行和7列中的已知数3、5对六宫排除,得到在E8和F8两格形成了一个数对,该数对排斥其他数字填入这两格。这时再利用D4和F1两格中的7对六宫进行排除,得到六宫中只有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":"唯余法就是利用数独中每格内都只有9种数字的可能性,如果某格中有8种数字都不能填,只能填入唯一未出现数字的方法。技巧示意图:","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":"","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":"如上图所示,C行有已知数1、","id":""},{"type":"text","text":Ŗ ,三","id":""},{"type":"text","text":"宫有已知数3、4、5 ,9列有已知数5、6、7、8 ,上述8种不同的数字,同时对C9格产生影响,使得C9格不能填入这8种数字,得到C9格内只能填入数字9,否则就出现同行、同列或同宫中数字相同的情况。","id":""}],"text":"","id":"doxcnioEc0UGQ6UIeeoE4anndIh"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列区块法","id":""}],"text":"","id":"doxcngOKiCumGmssEK45PeH2Ekg"},{"type":"paragraph","children":[{"type":"text","text":"行列区块法指的是利用行列排除,在某行或列内制造出一个区块,利用该区块对该区块所在宫的其他格进行删除的方法。技巧示意图:","id":""}],"text":"","id":"doxcnQ44KSsA2o6KI4lKyQ1h17t"},{"type":"image","attrs":{"height":415,"note":[{"type":"text","text":"行列区块法","id":""}],"url":"","width":439},"text":"","id":"doxcnO6cWgicy88SucLGXwyCkBf"},{"type":"paragraph","children":[{"type":"text","text":" 行列区块发","id":""}],"text":"","id":"doxcnWGCeu4G400KaIZnEwbMxLd"},{"type":"paragraph","children":[{"type":"text","text":"如上图所示,A9和12两格的1对5列进行排除,使得5列的1只能在D5、E5和F5三格之中,这时在5列内制造了一个含5的区块,该区块同时也存在于五直中,所以可以排除掉五宫其它格中的1。这时再结合D行和6列的已知数字,可以唯余得到D6格内只能填入9 。","id":""}],"text":"","id":"doxcneYeSCYiCg6GiKCyjUtyyHb"},{"type":"heading","attrs":{"level":2},"children":[{"type":"text","text":"行列内数对占位法","id":""}],"text":"","id":"doxcnEYs2AkacMCqW0qLhW9j3fk"},{"type":"paragraph","children":[{"type":"text","text":"数对占位法,在上面的宫内数对占位法中,我们已经学过数又寸占位法,这里讲的是数对出现行列里的情况,这时的观察难度会大大增加,本技巧也属于难度较大的技巧之一。技巧示意 图: ","id":""}],"text":"","id":"doxcnSKw48WeA2Ek4iGuRixfUah"},{"type":"image","attrs":{"height":422,"note":[{"type":"text","text":"行列内数对占位法","id":""}],"url":"","width":396},"text":"","id":"doxcnscC4IaKggeEYgpanK2M2lh"},{"type":"paragraph","children":[{"type":"text","text":"如图所示,利用四宫和8列的已知数2、7,同时对F行进行排除,在F有得到数字2、7只能填在F6和F9两格内,这时在F行的这两格内形成2、7数对。再观察A7和H8两格的8对六宫的排除","id":""},{"type":"text","text":",","id":""},{"type":"text","text":"六宫内只有E9格内可以填入8。","id":""}],"text":"","id":"doxcnkaM4uwISa26EAHkC3HVHGd"},{"type":"paragraph","children":[{"type":"text","text":"好了,如果你已经熟练掌握了上规则和技巧,就可以小试身手啦!","id":""}],"text":"","id":"doxcns4w02IGMGAiG4sxIPTuwob"},{"type":"paragraph","children":[{"type":"text","text":"","id":""}],"text":"","id":"doxcnOWME4GiyiWWQT0A5wtXBgf"}]%3C%2Fhowto_content%3E