Substitute each of the letters by a different digit from 0 to 9 to satisfy this system of alphametic equations. None of the numbers as well as none of the exponents contains a leading zero.

• (DID)^W = F^XA, and:
• (FLY)^A = Y^LI, and:
• (LOW)^O = I^LT

using the following code
digs = Table[i, {i, 0, 9}];
prms = Permutations[digs];
cnt = 0;
lng = Length[prms];
For[pi = 1, pi <= lng, ++pi,
  lst = prms[[pi]];
  d = lst[[1]];
  i = lst[[2]];
  w = lst[[3]];
  f = lst[[4]];
  x = lst[[5]];
  a = lst[[6]];
  l = lst[[7]];
  y = lst[[8]];
  o = lst[[9]];
  t = lst[[10]];
  If[a == 0 || o == 0 || t == 0,
   did = FromDigits[{d, i, d}];
   xa = FromDigits[{x, a}];
   fly = FromDigits[{f, l, y}];
   li = FromDigits[{l, i}];
   low = FromDigits[{l, o, w}];
   lt = FromDigits[{l, t}];
   If[did^w == f^xa && fly^a == y^li && low^o == i^lt,
    ++cnt;
    Print["Solution ", cnt, ":"];
    Print[did, "^", w, "=", f, "^", xa, "=", f^xa];
    Print[fly, "^", a, "=", y, "^", li, "=", y^li];
    Print[low, "^", o, "=", i, "^", lt, "=", i^lt];
    ];
   ];
  ];

gives the following lone solution
343^6=7^18=1628413597910449

729^8=9^24=79766443076872509863361

256^5=4^20=1099511627776

Posted by Daniel on 2010-08-05 11:52:53