# Solution to Maths

### by Oliver Kosut

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*