# Off Topic: Puzzle

Jim Hurley jhurley at infostations.com
Sun May 18 13:09:01 EDT 2003

```>
>Raoger Guay wrote:
>Hello Jim.
>
>This puzzle intrigued me enough to use RunRev to solve it.  I wasn't
>clever enough to solve it algebraically, so I wrote a script that
>incremented the two temperature over a reasonable range and analyzed
>the number characters of each increment to find the answer.  Works
>great and it was a fun exercise.
>
>Cheers, Roger
>

Hi Roger,

Programmers have problem solving built into their DNA. It's their
(our) idea of fun. Others do crossword puzzles and the Jumble.

Don't worry that you didn't find an algebraic solution. The algebraic
statement of the problem would look something like  this:

n + 10*m = 5/9 (m + 10*n -32)

This is one equation with two unknowns and so has no well defined,
unique algebraic solution. The additional condition that n and m are
integers, is a further constraint, and so there may be well defined
solutions and these are generally obtained by the method of
"exhaustion," that is trying all reasonable alternatives. So your
approach was the reasonable one.

Coincidentally, I have NPR on the radio right now, and the Tappet
brothers just gave the solution. They mentioned another simpler,
empirical technique: Get an analog thermometer with both the Celsius
and Fahrenheit scales. Just look for common temperatures where the
digits are reversed. Might  be a little tricky, since you are looking
for the rounded numbers reported by the digital thermometer.

Jim

```

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