Re: Well, I'll be damned...(even better!)

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: : : There's actually two of 'em: : : : 1+6+7+17+18+23 = 2+3+11+13+21+22 : : : 2+7+8+18+19+24 = 3+4+12+14+22+23 : : Yep; actually, the "basic or native" solution is the 1st one; : : if you increase the limit to 25, you'll also get: : : 3+8+9+19+20+25 = 4+5+13+15+23+ 24 : : ....and so on infinitely! : : : : : Takes my pc just under 10 seconds to get the first one, another 14 seconds : : : to the next, and about 38 seconds to finish. : : Wow! Takes mine a bit over 2 minutes (old 486!). : : Your "looping" sure beats mine, then. : : What does your looping look like, from g to k ? (I calculate L). : I wasn't completely satisfied with that one, so I cleaned it up a bit more. With the new, improved version, lap (11 6 7 17 18 23 / 2 3 11 13 21 22) is 5.06 seconds, lap 2 (2 7 8 18 19 24 / 3 4 12 14 22 23 6.44 seconds, lap 3 (just finishing up) 7.99 seconds. Total 19.49 seconds. Saved a few years. :) : Here's the code. Sorry, it's in C++. If anything's not clear, just ask. Hopefully, I put in enough extra spaces so my < 's don't get interpreted as HTML tags by the message board program. Otherwise I'll just try, try again. : #include < iostream.h> // that's just boilerplate for i/o functions : int main() : { : int a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,sum,sum2=0,lh[24]; : // just keep in mind that in C the convention : // is to start counting at 0, not 1 : for(m=0;m< 19;m++) : {a=m+1; : for(n=a;n< 20;n++) : {b=n+1; : for(o=b;o< 21;o++) : {c=o+1; : for(p=c;p< 22;p++) : {d=p+1; : for(q=d;q< 23;q++) : {e=q+1; : for(r=e;r< 24;r++) : if((sum=a+b+c+d+e+r+1)< 112) : {f=r+1; : // The lh[] array records the numbers chosen for : // a through f. This loop initializes it to 0. : for(y=0;y< 24;y++) : lh[y]=0; : // Now store a - f for this iteration. C arrays : // start with element 0, hence a-1, b-1, etc. : lh[a-1]=1;lh[b-1]=1;lh[c-1]=1;lh[d-1]=1;lh[e-1]=1;lh[f-1]=1; : // start looping g where a left off - no need : // to have g-l duplicate a-f : // also, if sum2 (g through l) is greater than : // sum (a through f), skip to next a-f set : for(s=a,sum2=0;s< 19&&!(sum2>sum);s++) : if(!lh[s]) : {g=s+1; : for(t=g;t< 20;t++) : if(!lh[t]) : {h=t+1; : for(u=h;u< 21;u++) : if(!lh[u]) : {i=u+1; : for(v=i;v< 22;v++) : if(!lh[v]) : {j=v+1; : for(w=j;w< 23;w++) : if(!lh[w]) : {k=w+1; : for(x=k,sum2=0;x< 24&&!(sum2>sum);x++) : {sum2=g+h+i+j+k+x+1; : if(!lh[x]) : {l=x+1; : if(sum2==sum) : if(a*a+b*b+c*c+d*d+e*e+f*f==g*g+h*h+i*i+j*j+k*k+l*l) : if(a*a*a+b*b*b+c*c*c+d*d*d+e*e*e+f*f*f : ==g*g*g+h*h*h+i*i*i+j*j*j+k*k*k+l*l*l) : if(a*a*a*a+b*b*b*b+c*c*c*c+d*d*d*d+e*e*e*e+f*f*f*f : ==g*g*g*g+h*h*h*h+i*i*i*i+j*j*j*j+k*k*k*k+l*l*l*l) : if(a*a*a*a*a+b*b*b*b*b+c*c*c*c*c+d*d*d*d*d+e*e*e*e*e : +f*f*f*f*f==g*g*g*g*g+h*h*h*h*h+i*i*i*i*i+j*j*j*j*j : +k*k*k*k*k+l*l*l*l*l) : { cout < < a < < " " < < b < < " " < < c < < " " < < d : << " " << e < < " " < < f < < endl; : cout < < g << " " < < h < < " " < < i < < " " < < j : < < " " < < k < < " " < < l < < endl; : } : }}}}}}}}}}}}} : return 0; : }

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