Calcrostic Puzzle

We call these problems calcrostic because they are showing calculations in a form similar to acrostic word puzzles. The color in the puzzle is used to indicate the computations in the rows, columns and diagonals. In a calcrostic, like

                       ab × cd = ebaf
                        + ×  ÷ ÷    −
                      egf ×  h =  hdc
                        = =  = =    =
                      ejc ×  k =  bfj

each letter represents a digit (one of 0,1,2,3,4,5,6,7,8,9). Equal letters represent equal digits, different letters represent different digits. The 9 resulting numbers ab, cd, ebaf, egf, h, hdc, ejc, k, bfj may have more than one digit (for example, ab is a 2-digit number) and are arranged in a 3 × 3 square as above. These numbers satisfy 3 horizontal, 3 vertical and 2 diagonal relations (like the diagonal relation ab × h = bfj where × stands for multiplication and ÷ for division. The problem is to find the value of each letter.

For example, the puzzle above has the solution

                       54 × 27 = 1458
                        + ×  ÷ ÷    −
                      108 ×  9 =  972
                        = =  = =    =
                      162 ×  3 =  486

Simpler versions of this type of puzzle will appear in future caribou contests, starting January 2010.

Have fun!