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解题方法趣谈 ——巧填等式题解  

2016-07-28 07:46:40|  分类: 教育 |  标签: |举报 |字号 订阅

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巧填等式题解                                                                              【题】一、请将“12345678”八个数码分别填入下列各组:                              1 1+ + =9+ + =8+ + =6+ +                           2 1+ + =9+ + =7+ + =3+ +                     二、请将“1112131415161718”八个数码分别填入下式:                                1+ + =9+ + =8+ + =6+ +                         三、从上列题解能总结出什么规律?请简述之。                                                     【解】:                                                                                                                              一、1                                                                                                                            先算总数:(1+2+3+4+5+6+7+8+1+9+8+6=60                                                   式中有四个相等的部分,每部分总数等于60的四分之一,即是15                             再减去每部分已知数,余下的数为每部分的两个未知数之和,分别是:14679     再分别进行等式分解:14=(1+13=2+12=3+11=4+10=5+9=6+8=7+7   (括号内有8以上的数,可排除;)                                                                                                           6=1+5=2+4=3+3                                                                                                             7=1+6=2+5=3+4                                                                                                             9=1+8=2+7=3+6=4+5                                                                                                     括号内有8以上的数,可排除,筛选得:                                                        14=6+86=1+57=3+49=2+7                                                                                    顺序填入68153427,即解。                                                                                                【解】                                                                                                                           一、2                                                                                                                         先算总数:(1+2+3+4+5+6+7+8+1+9+7+3=56                                                       式中有四个相等的部分,每部分总数等于56的四分之一,即是14                                 再减去每部分已知数,余下的数为每部分的两个未知数之和,分别是:135711    再分别进行等式分解:                                                                             13=(1+12=2+11=3+10=4+9=5+8=6+7                                                                           5=1+4=2+3                                                                                                                    7=1+6=2+5=3+4                                                                                                             11=1+10==2+9==3+8=4+7=5+6                                                                                       括号内有8以上的数,可排除,筛选得:                                                     13=5+8=6+7                                                                                                     5=1+4=2+3                                                                                                                    7=1+6=2+5=3+4                                                                                                             11=3+8=4+7=5+6                                                                                                           顺序填入:58231647,即解。                                                               一、1 1+6+8=9+1+5=8+3+4=6+2+7                           2 1+5+8=9+2+3=7+1+6=3+4+7                    【解】                                                                                                                           二的答案:1+16+18=9+11+15=8+13+14=6+12+17  【解】                                                                                                                           三的简答:因为等式的四部分相等;总数是定数;每个数都可以分解成若干个数之和,所以可用总分法来解。总数=(11+12+13=14+15+16+17+18)+(1+9+8+6)=116+24=140               140四等分,每部分为35。再减去每部分已知数,余下的数为每部分的两个未知数之和,分别是34262729。再进行等式分解。       34=1+33=2+32=3+31=4+30=5+29=6+28=7+27=8+26=9+25=10+24=11+23=12+22=13+21=14+20=15+19=16+18=17+17 排除不合要求的,34=11+23=12+22=13+21=14+20=15+19=16+18=17+17                                                            26=1+25=2+24=3+23=4+22=5+21=6+20=7+19=8+18=9+17=10+16=11+15=12+14=13+13,排除不合要求的,26=8+18=9+17=10+16=11+15=12+14=13+13                                    27=1+26=2+25=3+24=4+23=5+22=6+21=7+20=8+19=9+18=10+17=11+16=12+15=13+14,排除不合要求的,27=9+18=10+17=11+16=12+15=13+14                                             29=1+28=2+27=3+26=4+25=5=24=6+23=7+22=8+21=9+20=10+19=11+18=12+17=13+16=14+15,排除不合要求的,29=11+18=12+17=13+16=14+15                                                   试逐一代入可得解。

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