On my way to work, I pass by a digital thermometer outside a bank that displays the temperature to the nearest integer, alternating back and forth between Fahrenheit and Celsius at four-second intervals.

The other day, when I was going to work, I noticed that the temperatures displayed in Fahrenheit and Celsius were simply reverse digits of each other.

Well, it warmed up nicely during the day, and when I was on my way home, I looked at the same thermometer.
Imagine my shock when, again, the Fahrenheit and Celsius temperature displays were simply reversed digits of each other!

What was the temperature when I came in to work, and what was it when I was on my way home?

Note: To convert from degrees Fahrenheit to Celsius, subtract 32 then multiply by 5/9. To convert the other way, simply do the opposite (multiply by 9/5 and add 32). Ignore leading zeroes.

I figured out this problem by taking the two digits and making a two variable equation.
(10x+y-32)5/9=10y+x
After a lot of simplification, I got something close to 1/2*x-2=y. So I tested a few inputs of x that would give integers, and 61F and 82F came close to being their reflections in C. So it was 61F on the way to work and 82F back.

Posted by Tristan on 2003-09-29 18:24:23