Solve this alphametic integral puzzle, where each of the capital letters in bold represents a different decimal digit from 0 to 9, given that C and N are constants and, E is not zero.

B
∫ C*x^N dx = EDGE
A

I used the following Mathematica code to find the only solution of

A=0 B=6 C=8 N=3 E=2 D=5 G=9

For[a=0,a£9,a++,

For[b=0,b£9,b++,

If[b¹a,

For[c=0,c£9,c++,

If[c¹a && c¹b,

For[n=0,n£9,n++,

If[n¹a && n¹b && n¹c,

For[e=1,e£9,e++,

If[e¹a && e¹b && e¹c && e¹n,

For[d=0,d£9,d++,

If[d¹a && d¹b && d¹c && d¹n && d¹e,

For[g=0,g£9,g++,

If[g¹a && g¹b && g¹c && g¹n && g¹e && g¹d,

x1=c*(b^(n+1)-a^(n+1))/(n+1);

x2=e+10*g+100*d+1000*e;

If[x1Šx2,

Print[a,",",b,",",c,",",n,",",e,",",d,",",g];

];

];

];

];

];

];];];];];];];];];

Posted by Daniel on 2009-03-25 13:11:15