In this puzzle, each of the four arithmetic operations is its own cryptarithm. That is, each digit shown represents a particular (usually different) digit, and each operation has its own such mapping. When this remapping is performed, all the arithmetic statements become correct. For instance, 4+6=91 really represents 5+7=12, and so in sums, each 4 represents a 5, each 6 a 7, etc. The four mappings are (where "visible" is the digits as they appear in the puzzle, and "real" what they represent, to make things correct):
+: Visible 0123456789 Real 6243587901 -: Visible 0123456789 Real 6437095821 *: Visible 0123456789 Real 8540269713 /: Visible 0123456789 Real 5907326418
Once these are deduced, the solution comes out of the expression at the bottom, which needs to be evaluated using the "redefined" operations. That is, to calculate 17+17, you use the sum mapping, so it really represents 29+29=58, which you convert back to "visible" to get 45. Similarly, 17*17*17, using the multiplication mapping, becomes 801869. Then you perform 801869/45 using the division mapping, even though those numbers originally came from the sum and multiplication mappings. So this represents 159168/32=4974, which maps back to 7137.
Continuing this, the entire expression becomes (again, in "visible") 2005120520251605. Looking at this two digits at a time and mapping to letters gives the answer TELETYPE.
2006 MIT Mystery Hunt