The Temperature Flip

Oct 03, 2020

RAY: Stevie decides to take his motorcycle to work to enjoy the nice warm, sunny weather. On his way there he looks up and sees one of those big signs that display the time and temperature. The temperature comes up in Fahrenheit, and a few seconds later it comes up in centigrade. Stevie says, "Hah! That's interesting. The digits are exactly reversed." For example, it might have read 31 degrees Fahrenheit, and when it showed the centigrade reading it said "13."

At the end of the day, when he comes out of work, he realizes he should have checked the weather forecast. It’s drizzly, rainy, and cold, and he has to get back on his motorcycle.

He's riding home when he comes to the same intersection. He thinks, "What are the chances I'd ever see that again?" He knows it's a different temperature because it's not warm and sunny anymore. He sees the temperature in Fahrenheit and the temperature in centigrade.

What are the chances? Only in a puzzler could this happen! The question is, what was the temperature in the morning when he went to work, and what was the temperature when he went home?

RAY: It turns out that in the morning when the sun was out and it was balmy, it was 28 degrees Celsius, which is 82 degrees Fahrenheit. At night when he came home and it was rainy, it was 16 degrees and 61 degrees.

It has to be between 50 and 99 Fahrenheit. Below 50 is 10 degrees Centigrade; you can't reverse the digits if it's nine degrees Centigrade. Between 50 and 99, these are the only temperatures where they're reversed.