# Solution to Maths

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