C语言四阶完美幻方.doc

/ 四阶幻方.cpp : Defines the entry point for the console application./* 操作系统：Windows XP * 编译环境：Microsoft Visual C+6.0 * * 程序编写：万传华 * 联系邮箱： */求解幻方/ x11 x12 x13 x14/ x21 x22 x23 x24/ x31 x32 x33 x34/ x41 x42 x43 x44/由于已知四阶幻方数量很多，总数是880*8=7040，/故在此只求完美幻方/ x11+x12+x13+x14=34/ x21+x22+x23+x24=34/ x31+x32+x33+x34=34/ x41+x42+x43+x44=34/ x11+x21+x31+x41=34/ x12+x22+x32+x42=34/ x13+x23+x33+x43=34/ x14+x24+x34+x44=34/ x11+x22+x33+x44=34/ x14+x23+x32+x41=34/还有泛对角线/ x21+x32+x43+x14=34/ x31+x42+x13+x24=34/ x41+x12+x23+x34=34/ x11+x24+x33+x42=34/ x12+x21+x34+x43=34/ x13+x22+x31+x44=34/#include stdafx.h#include#include #include #include #include void show(int *M,unsigned rows,unsigned cols)printf(n);for(unsigned i=0;irows;+i)for(unsigned j=0;ja的情况if(ba)c=a,a=b,b=c;doc=a%b,a=b,b=c;while(c);return a;/整数型方程/方程数FCS1，未知数WZS1，FCS=FCS) break;if(t=FCS)+col;continue;if(P!=Q)/交换for(j=0;jWZS;+j)k=Pj;Pj=Qj;Qj=k;z=Pcol;/参考数位置：row行,col列/消元for(i=row+1,Q=P+WZS;iFCS;+i,Q+=WZS)/第i行y=Qcol;if(y=0) continue;k=gcd(abs(z),abs(y);x=z/k,y/=k;for(j=0;jWZS;+j)/第j列Qj=Qj*x-Pj*y;/show(M,FCS,WZS);/调试输出/getch();+row,+col,P+=WZS;while(rowFCS & col=WZS) break;if(col=WZS)continue;/简化for(j=0;jWZS;+j)x=Pj;if(x!=0) break;if(x!=0)x=abs(x);for(;j1)for(j=0;jWZS;+j)Pj/=x;/消元z=Pcol;Q=P-WZS;i=row;while(i-)/第i行,i=0,row)y=Qcol;if(y!=0)k=gcd(abs(z),abs(y);x=z/k,y/=k;for(j=0;j0 & col0);/N阶幻方void init(int *M,unsigned N)unsigned i,j,t;int *P,*Q;int x=(int)(N*N);x=-(x*x+x)/(int)N/2);/清零for(i=0,P=M;iN*4;+i,P+=N*N+1)for(j=0;jN*N+1;+j)Pj=0;/N行和,0,N)for(i=0,P=M;iN;+i,P+=N*N+1)for(Q=P+i*N,t=0;tN;+t)Qt=1;/N列和,N,N*2)for(i=0;iN;+i,P+=N*N+1)for(Q=P+i,t=0;tN;+t,Q+=N)Q0=1;/对角线for(i=0;iN;+i,P+=N*N+1)/起点(i,0)for(j=i,Q=P+i*N,t=0;t=N)j=0;Q-=N*N;/对角线/for(i=0;iN;+i,P+=N*N+1)for(j=N-i-1,Q=P+j,t=0;tN;+t)Q0=1;Q+=N-1;if(j=0)j=N-1;Q+=N;else-j;/处理常数i=N*4;P=M;while(i-)PN*N=x;P+=N*N+1;/列移位void move(int *M,unsigned rows,unsigned cols,unsigned from,unsigned to)unsigned i;int *P,*Q,t;for(i=0,P=M+from,Q=M+to;irows;+i,P+=cols,Q+=cols)t=*P,*P=*Q,*Q=t;void huajian()const unsigned N=4;const unsigned fcs=N*4;const unsigned wzs=N*N;int Mfcswzs+1=/* x11,x12,x13,x14,x21,x22,x23,x24,x311,x32,x33,x34,x41,x42,x43,x441, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34,0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -34,0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -34,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -34,1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -34,0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -34,0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -34,0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, -34,1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -34,0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -34,0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, -34,0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -34,0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -34,0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -34,0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -34,1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, -34,*/x11,x12,x13,x41,x21,x22,x23,x24,x311,x32,x33,x34,x14,x42,x43,x441, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -34,0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -34,0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, -34,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, -34,1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -34,0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -34,0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, -34,0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, -34,1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, -34,0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, -34,0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, -34,0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, -34,0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, -34,0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, -34,0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -34,1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, -34,;/init(&M00,N);/show(&M00,fcs,wzs+1);/move(&M00,fcs,wzs+1,3,12);/move(&M00,fcs,wzs+1,11,13);/show(&M00,fcs,wzs+1);Equation(&M00,fcs,wzs);show(&M00,fcs,wzs+1);/*结果x11,x12,x13,x41,x21,x22,x23,x24,x311,x32,x33,x34,x14,x42,x43,x441, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0,0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 0,0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, -34,0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -34,0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -17,0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -17,0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 17,0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, -17,0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 1, 1, -17,0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 17,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 1, 1, 0, -17,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0, 1, -17,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,*/void test()int count=0;int flag17=0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;int x11,x12,x13,x14,x21,x22,x23,x24,x31,x32,x33,x34,x41,x42,x43,x44;for(x14=1;x1417;+x14)if(flagx14) continue;x32=17-x14;if(flagx32) continue;flagx14=true;flagx32=true;for(x42=1;x4217;+x42)if(flagx42) continue;x24=17-x42;if(flagx24) continue;flagx24=true;flagx42=true;for(x43=1;x4317;+x43)if(flagx43) continue;x21=17-x43;if(flagx21) continue;flagx43=true;flagx21=true;x11=x42+x43-x14;if(x1116 | flagx11) goto err11;flagx11=true;x33=17+x14-x42-x43;if(x3316 | flagx33) goto err33;flagx33=true;for(x44=1;x4417;+x44)if(flagx44) continue;x22=17-x44;if(flagx22) continue;flagx44=true;flagx22=true;x12=x14+x44-x42;if(x1216 | flagx12) goto err12;flagx12=true;x13=34-x14-x43-x44;if(x1316 | flagx13) goto err13;flagx13=true;x41=34-x42-x43-x44;if(x4116 | flagx41) goto err41;flagx41=true;x23=x42+x43+x44-17;if(x2316 | flagx23) goto err23;flagx23=true;x31=x14+x43+x44-17;if(x3116 | flagx31) goto err31;flagx31=true;x34=17+x42-x14-x44;if(x3416 | flagx34) goto err34;printf(第%03d解：%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2d,%2dn,+count,x11,x12,x13,x14,x21,x22,x23,x24,x31,x32,x33,x34,x41,x42,x43,x44);/if(count100) return;err34:flagx31=false;err31:flagx23=false;err23:flagx41=false;err41:flagx13=false;err13:flagx12=false;err12:flagx22=false;flagx44=false;flagx33=false;err33:flagx11=false;err11:flagx21=false;flagx43=false;flagx24=false;flagx42=false;flagx32=false;flagx14=false;printf(n共找到%d解n,count);int main(int argc, char* argv)/huajian();test();return 0;/*四阶完美幻方第001解： 8,11,14, 1,10, 5, 4,15, 3,16, 9, 6,13, 2, 7,12第002解： 8,13,12, 1,10, 3, 6,15, 5,16, 9, 4,11, 2, 7,14第003解：12, 7,14, 1, 6, 9, 4,15, 3,16, 5,10,13, 2,11, 8第004解：12,13, 8, 1, 6, 3,10,15, 9,16, 5, 4, 7, 2,11,14第005解：14, 7,12, 1, 4, 9, 6,15, 5,16, 3,10,11, 2,13, 8第006解：14,11, 8, 1, 4, 5,10,15, 9,16, 3, 6, 7, 2,13,12第007解： 8,10,15, 1,11, 5, 4,14, 2,16, 9, 7,13, 3, 6,12第008解： 8,13,12, 1,11, 2, 7,14, 5,16, 9, 4,10, 3, 6,15第009解：12, 6,15, 1, 7, 9, 4,14, 2,16, 5,11,13, 3,10, 8第010解：12,13, 8, 1, 7, 2,11,14, 9,16, 5, 4, 6, 3,10,15第011解：15, 6,12, 1, 4, 9, 7,14, 5,16, 2,11,10, 3,13, 8第012解：15,10, 8, 1, 4, 5,11,14, 9,16, 2, 7, 6, 3,13,12第013解： 8,10,15, 1,13, 3, 6,12, 2,16, 9, 7,11, 5, 4,14第014解： 8,11,14, 1,13, 2, 7,12, 3,16, 9, 6,10, 5, 4,15第015解：14, 4,15, 1, 7, 9, 6,12, 2,16, 3,13,11, 5,10, 8第016解：14,11, 8, 1, 7, 2,13,12, 9,16, 3, 6, 4, 5,10,15第017解：15, 4,14, 1, 6, 9, 7,12, 3,16, 2,13,10, 5,11, 8第018解：15,10, 8, 1, 6, 3,13,12, 9,16, 2, 7, 4, 5,11,14第019解：12, 6,15, 1,13, 3,10, 8, 2,16, 5,11, 7, 9, 4,14第020解：12, 7,14, 1,13, 2,11, 8, 3,16, 5,10, 6, 9, 4,15第021解：14, 4,15, 1,11, 5,10, 8, 2,16, 3,13, 7, 9, 6,12第022解：14, 7,12, 1,11, 2,13, 8, 5,16, 3,10, 4, 9, 6,15第023解：15, 4,14, 1,10, 5,11, 8, 3,16, 2,13, 6, 9, 7,12第024解：15, 6,12, 1,10, 3,13, 8, 5,16, 2,11, 4, 9, 7,14第025解： 7,12,13, 2, 9, 6, 3,16, 4,15,10, 5,14, 1, 8,11第026解： 7,14,11, 2, 9, 4, 5,16, 6,15,10, 3,12, 1, 8,13第027解：11, 8,13, 2, 5,10, 3,16, 4,15, 6, 9,14, 1,12, 7第028解：11,14, 7, 2, 5, 4, 9,16,10,15, 6, 3, 8, 1,12,13第029解：13, 8,11, 2, 3,10, 5,16, 6,15, 4, 9,12, 1,14, 7第030解：13,12, 7, 2, 3, 6, 9,16,10,15, 4, 5, 8, 1,14,11第031解： 7, 9,16, 2,12, 6, 3,13, 1,15,10, 8,14, 4, 5,11第032解： 7,14,11, 2,12, 1, 8,13, 6,15,10, 3, 9, 4, 5,16第033解：11, 5,16, 2, 8,10, 3,13, 1,15, 6,12,14, 4, 9, 7第034解：11,14, 7, 2, 8, 1,12,13,10,15, 6, 3, 5, 4, 9,16第035解：16, 5,11, 2, 3,10, 8,13, 6,15, 1,12, 9, 4,14, 7第036解：16, 9, 7, 2, 3, 6,12,13,10,15, 1, 8, 5, 4,14,11第037解： 7, 9,16, 2,14, 4, 5,11, 1,15,10, 8,12, 6, 3,13第038解： 7,12,13, 2,14, 1, 8,11, 4,15,10, 5, 9, 6, 3,16第039解：13, 3,16, 2, 8,10, 5,11, 1,15, 4,14,12, 6, 9, 7第040解：13,12, 7, 2, 8, 1,14,11,10,15, 4, 5, 3, 6, 9,16第041解：16, 3,13, 2, 5,10, 8,11, 4,15, 1,14, 9, 6,12, 7第042解：16, 9, 7, 2, 5, 4,14,11,10,15, 1, 8, 3, 6,12,13第043解：11, 5,16, 2,14, 4, 9, 7, 1,15, 6,12, 8,10, 3,13第044解：11, 8,13, 2,14, 1,12, 7, 4,15, 6, 9, 5,10, 3,16第045解：13, 3,16, 2,12, 6, 9, 7, 1,15, 4,14, 8,10, 5,11第046解：13, 8,11, 2,12, 1,14, 7, 6,15, 4, 9, 3,10, 5,16第047解：16, 3,13, 2, 9, 6,12, 7, 4,15, 1,14, 5,10, 8,11第048解：16, 5,11, 2, 9, 4,14, 7, 6,15, 1,12, 3,10, 8,13第049解： 6,12,13, 3, 9, 7, 2,16, 4,14,11, 5,15, 1, 8,10第050解： 6,15,10, 3, 9, 4, 5,16, 7,14,11, 2,12, 1, 8,13第051解：10, 8,13, 3, 5,11, 2,16, 4,14, 7, 9,15, 1,12, 6第052解：10,15, 6, 3, 5, 4, 9,16,11,14, 7, 2, 8, 1,12,13第053解：13, 8,10, 3, 2,11, 5,16, 7,14, 4, 9,12, 1,15, 6第054解：13,12, 6, 3, 2, 7, 9,16,11,14, 4, 5, 8, 1,15,10第055解： 6, 9,16, 3,12, 7, 2,13, 1,14,11, 8,15, 4, 5,10第056解： 6,15,10, 3,12, 1, 8,13, 7,14,11, 2, 9, 4, 5,16第057解：10, 5,16, 3, 8,11, 2,13, 1,14, 7,12,15, 4, 9, 6第058解：10,15, 6, 3, 8, 1,12,13,11,14, 7, 2, 5, 4, 9,16第059解：16, 5,10, 3, 2,11, 8,13, 7,14, 1,12, 9, 4,15, 6第060解：16, 9, 6, 3, 2, 7,12,13,11,14, 1, 8, 5, 4,15,10第061解： 6, 9,16, 3,15, 4, 5,10, 1,14,11, 8,12, 7, 2,13第062解： 6,12,13, 3,15, 1, 8,10, 4,14,11, 5, 9, 7, 2,16第063解：13, 2,16, 3, 8,11, 5,10, 1,14, 4,15,12, 7, 9, 6第064解：13,12, 6, 3, 8, 1,15,10,11,14, 4, 5, 2, 7, 9,16第065解：16, 2,13, 3, 5,11, 8,10, 4,14, 1,15, 9, 7,12, 6第066解：16, 9, 6, 3, 5, 4,15,10,11,14, 1, 8, 2, 7,12,13第067解：10, 5,16, 3,15, 4, 9, 6, 1,14, 7,12, 8,11, 2,13第068解：10, 8,13, 3,15, 1,12, 6, 4,14, 7, 9, 5,11, 2,16第069解：13, 2,16, 3,12, 7, 9, 6, 1,14, 4,15, 8,11, 5,10第070解：13, 8,10, 3,12, 1,15, 6, 7,14, 4, 9, 2,11, 5,16第071解：16, 2,13, 3, 9, 7,12, 6, 4,14, 1,15, 5,11, 8,10第072解：16, 5,10, 3, 9, 4,15, 6, 7,14, 1,12, 2,11, 8,13第073解： 5,11,14, 4,10, 8, 1,15, 3,13,12, 6,16, 2, 7, 9第074解： 5,16, 9, 4,10, 3, 6,15, 8,13,12, 1,11, 2, 7,14第075解： 9, 7,14, 4, 6,12, 1,15, 3,13, 8,10,16, 2,11, 5第076解： 9,16, 5, 4, 6, 3,10,15,12,13, 8, 1, 7, 2,11,14第077解：14, 7, 9, 4, 1,12, 6,15, 8,13, 3,10,11, 2,16, 5第078解：14,11, 5, 4, 1, 8,10,15,12,13, 3, 6, 7, 2,16, 9第079解： 5,10,15, 4,11, 8, 1,14, 2,13,12, 7,16, 3, 6, 9第080解： 5,16, 9, 4,11, 2, 7,14, 8,13,12, 1,10, 3, 6,15第081解： 9, 6,15, 4, 7,12, 1,14, 2,13, 8,11,16, 3,10, 5第082解： 9,16, 5, 4, 7, 2,11,14,12,13, 8, 1, 6, 3,10,15第083解：15, 6, 9, 4, 1,12, 7,14, 8,13, 2,11,10, 3,16, 5第084解：15,10, 5, 4, 1, 8,11,14,12,13, 2, 7, 6, 3,16, 9第085解： 5,10,15, 4,16, 3, 6, 9, 2,13,12, 7,11, 8, 1,14第086解： 5,11,14, 4,16, 2, 7, 9, 3,13,12, 6,10, 8, 1,15第087解：14, 1,15, 4, 7,12, 6, 9, 2,13, 3,16,11, 8,10, 5第088解：14,11, 5, 4, 7, 2,16, 9,12,13, 3, 6, 1, 8,10,15第089解：15, 1,14, 4, 6,12, 7, 9, 3,13, 2,16,10, 8,11, 5第090解：15,10, 5, 4, 6, 3,16, 9,12,13, 2, 7, 1, 8,11,14第091解： 9, 6,15, 4,16, 3,10, 5, 2,13, 8,11, 7,12, 1,14第092解： 9, 7,14, 4,16, 2,11, 5, 3,13, 8,10, 6,12, 1,15第093解：14, 1,15, 4,11, 8,10, 5, 2,13, 3,16, 7,12, 6, 9第094解：14, 7, 9, 4,11, 2,16, 5, 8,13, 3,10, 1,12, 6,15第095解：15, 1,14, 4,10, 8,11, 5, 3,13, 2,16, 6,12, 7, 9第096解：15, 6, 9, 4,10, 3,16, 5, 8,13, 2,11, 1,12, 7,14第097解： 4,14,11, 5, 9, 7, 2,16, 6,12,13, 3,15, 1, 8,10第098解： 4,15,10, 5, 9, 6, 3,16, 7,12,13, 2,14, 1, 8,11第099解：10, 8,11, 5, 3,13, 2,16, 6,12, 7, 9,15, 1,14, 4第100解：10,15, 4, 5, 3, 6, 9,16,13,12, 7, 2, 8, 1,14,11第101解：11, 8,10, 5, 2,13, 3,16, 7,12, 6, 9,14, 1,15, 4第102解：11,14, 4, 5, 2, 7, 9,16,13,12, 6, 3, 8, 1,15,10第103解： 4, 9,16, 5,14, 7, 2,11, 1,12,13, 8,15, 6, 3,10第104解： 4,15,10, 5,14, 1, 8,11, 7,12,13, 2, 9, 6, 3,16第105解：10, 3,16, 5, 8,13, 2,11, 1,12, 7,14,15, 6, 9, 4第106解：10,15, 4, 5, 8, 1,14,11,13,12, 7, 2, 3, 6, 9,16第107解：16, 3,10, 5, 2,13, 8,11, 7,12, 1,14, 9, 6,15, 4第108解：16, 9, 4, 5, 2, 7,14,11,13,12, 1, 8, 3, 6,15,10第109解： 4, 9,16, 5,15, 6, 3,10, 1,12,13, 8,14, 7, 2,11第110解： 4,14,11, 5,15, 1, 8,10, 6,12,13, 3, 9, 7, 2,16第111解：11, 2,16, 5, 8,13, 3,10, 1,12, 6,15,14, 7, 9, 4第112解：11,14, 4, 5, 8, 1,15,10,13,12, 6, 3, 2, 7, 9,16第113解：16, 2,11, 5, 3,13, 8,10, 6,12, 1,15, 9, 7,14, 4第114解：16, 9, 4, 5, 3, 6,15,10,13,12, 1, 8, 2, 7,14,11第115解：10, 3,16, 5,15, 6, 9, 4, 1,12, 7,14, 8,13, 2,11第116解：10, 8,11, 5,15, 1,14, 4, 6,12, 7, 9, 3,13, 2,16第117解：11, 2,16, 5,14, 7, 9, 4, 1,12, 6,15, 8,13, 3,10第118解：11, 8,10, 5,14, 1,15, 4, 7,12, 6, 9, 2,13, 3,16第119解：16, 2,11, 5, 9, 7,14, 4, 6,12, 1,15, 3,13, 8,10第120解：16, 3,10, 5, 9, 6,15, 4, 7,12, 1,14, 2,13, 8,11第121解： 3,13,12, 6,10, 8, 1,15, 5,11,14, 4,16, 2, 7, 9第122解： 3,16, 9, 6,10, 5, 4,15, 8,11,14, 1,13, 2, 7,12第123解： 9, 7,12, 6, 4,14, 1,15, 5,11, 8,10,16, 2,13, 3第124解： 9,16, 3, 6, 4, 5,10,15,14,11, 8, 1, 7, 2,13,12第125解：12, 7, 9, 6, 1,14, 4,15, 8,11, 5,10,13, 2,16, 3第126解：12,13, 3, 6, 1, 8,10,15,14,11, 5, 4, 7, 2,16, 9第127解： 3,10,15, 6,13, 8, 1,12, 2,11,14, 7,16, 5, 4, 9第128解： 3,16, 9, 6,13, 2, 7,12, 8,11,14, 1,10, 5, 4,15第129解： 9, 4,15, 6, 7,14, 1,12, 2,11, 8,13,16, 5,10, 3第130解： 9,16, 3, 6, 7, 2,13,12,14,11, 8, 1, 4, 5,10,15第131解：15, 4, 9, 6, 1,14, 7,12, 8,11, 2,13,10, 5,16, 3第132解：15,10, 3, 6, 1, 8,13,12,14,11, 2, 7, 4, 5,16, 9第133解： 3,10,15, 6,16, 5, 4, 9, 2,11,14, 7,13, 8, 1,12第134解： 3,13,12, 6,16, 2, 7, 9, 5,11,14, 4,10, 8, 1,15第135解：12, 1,15, 6, 7,14, 4, 9, 2,11, 5,16,13, 8,10, 3第136解：12,13, 3, 6, 7, 2,16, 9,14,11, 5, 4, 1, 8,10,15第137解：15, 1,12, 6, 4,14, 7, 9, 5,11, 2,16,10, 8,13, 3第138解：15,10, 3, 6, 4, 5,16, 9,14,11, 2, 7, 1, 8,13,12第139解： 9, 4,15, 6,16, 5,10, 3, 2,11, 8,13, 7,14, 1,12第140解： 9, 7,12, 6,16, 2,13, 3, 5,11, 8,10, 4,14, 1,15第141解：12, 1,15, 6,13, 8,10, 3, 2,11, 5,16, 7,14, 4, 9第142解：12, 7, 9, 6,13, 2,16, 3, 8,11, 5,10, 1,14, 4,15第143解：15, 1,12, 6,10, 8,13, 3, 5,11, 2,16, 4,14, 7, 9第144解：15, 4, 9, 6,10, 5,16, 3, 8,11, 2,13, 1,14, 7,12第145解： 2,13,12, 7,11, 8, 1,14, 5,10,15, 4,16, 3, 6, 9第146解： 2,16, 9, 7,11, 5, 4,14, 8,10,15, 1,13, 3, 6,12第147解： 9, 6,12, 7, 4,15, 1,14, 5,10, 8,11,16, 3,13, 2第148解： 9,16, 2, 7, 4, 5,11,14,15,10, 8, 1, 6, 3,13,12第149解：12, 6, 9, 7, 1,15, 4,14, 8,10, 5,11,13, 3,16, 2第150解：12,13, 2, 7, 1, 8,11,14,15,10, 5, 4, 6, 3,16, 9第151解： 2,11,14, 7,13, 8, 1,12, 3,10,15, 6,16, 5, 4, 9第152解： 2,16, 9, 7,13, 3, 6,12, 8,10,15, 1,11, 5, 4,14第153解： 9, 4,14, 7, 6,15, 1,12, 3,10, 8,13,16, 5,11, 2第154解： 9,16, 2, 7, 6, 3,13,12,15,10, 8, 1, 4, 5,11,14第155解：14, 4, 9, 7, 1,15, 6,12, 8,10, 3,13,11, 5,16, 2第156解：14,11, 2, 7, 1, 8,13,12,15,10, 3, 6, 4, 5,16, 9第157解： 2,11,14, 7,16, 5, 4, 9, 3,10,15, 6,13, 8, 1,12第158解： 2,13,12, 7,16, 3, 6, 9, 5,10,15, 4,11, 8, 1,14第159解：12, 1,14, 7, 6,15, 4, 9, 3,10, 5,16,13, 8,11, 2第160解：12,13, 2, 7, 6, 3,16, 9,15,10, 5, 4, 1, 8,11,14第161解：14, 1,12