Charlie and the Perplexing Temperature Billboard

Sep 26, 2005

RAY: This puzzler is from my Fahrenheit-Celsius series. It's from Mike Mercer, and I didn't really even have to obfuscate this at all! Here it is:

Charlie is heading off to work one fall morning, and as he does every morning, he passes a billboard that displays the current temperature in Fahrenheit in one corner, and the temperature in Celsius in the other corner.

He notices both temperatures, and thinks, 'It's a pretty nice day for late fall.' But, as the day progresses, a monstrous cold front hits town. On his way home, Charlie passes the temperature billboard again, and finds that the Fahrenheit temperature is now 36 degrees colder than it was that morning. So, when he drove in it was one temperature, and now it's that temperature minus 36.

But, when he looks at the Celsius temperature he's confused, because it reads exactly the same as it did that morning. Charlie figures that the display must be stuck, because it's certainly much colder on his ride home.

In fact, it was not stuck. But, there was indeed something wrong with the Celsius sign.

What was the problem and how cold was it?
TOM: The easy part is that the Celsius side lost the minus sign.

RAY: Exactly. So if it was 12 degrees Celsius in the morning, it would have to be minus 12.

RAY: Right. But 12 doesn't work, because to convert Fahrenheit to Celsius, the equation is F equals nine-fifths of C plus 32.

That's one equation. But to solve this puzzler, you need another equation. And here's the other equation: The temperature in degrees Fahrenheit minus 36 is equal to nine-fifths times the negative C temperature, plus 32.

With those two equations, namely:

F= 9/5C + 32 and
F-36 = 9/5 (-C) + 32

You can solve for F, because when you add those two equations together, you get 2F - 36 = 64, or F = 50.

So, 50 degrees Fahrenheit is ten degrees Celsius and 36 less than 50 is 14, which is minus 10 degrees Celsius. Pretty cute, huh? Who's our winner?

TOM: The winner is Jim Stegman from Grand Haven, Michigan, and for having his answer selected at random from among all the correct answers that we got Jim is going to get a 26-dollar gift certificate to the Shameless Commerce Division at with which he can get a Dewey, Cheatham and Howe T-shirt featuring a facsimile of our very own office window in Harvard Square, Cambridge.

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