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Temperature Reverse Digits: Extended Puzzler

The question was about a temperature sign where a driver noticed the digits were exactly reversed, comparing deg C vs deg F. 28/82 & 16/61 (C/F) were the two answers.

But those numbers are actually rounded to the nearest integer. 28 C = 82.4, and 16 C = 60.8.

Here’s an extended version of this puzzler: Are there any combinations in integer pairs that are exact matches? So only pairs that are exact integers are allowed,. 0 and 32 are an exact integer pair, as well as 100 and 212. There’s many others. From that list, are there any where the pair match up when reversed? I don’t think there are any solutions for positive 2 digit integers. Do you agree? If so, what about negative 2 digit integers? I don’t think there are any of those that work either. So what about 3 digit integer pairs? Any exact integer solutions this puzzler? If so , what’s the one w/the fewest digits.? Or is there even one at all?

I don’t know, just asking.

I started running an excel table to two decimal places with the formulas. But looking for the reverse matches made me crazy, so I gave up. My eyes got all buzzy and my brain almost exploded. :fearful:

I think there’s a way using Diophantine equations to find them, but the problem is I don’t know how to use Diophantine equations … lol … maybe I’ll check a book out of the library and take a crack at it , thanks for giving it a go yourself TMB!

I’m absolutely certain there’s a recognition program that’ll do this.
Unfortunately, I don’t have it!

I used excel to check the first 10000 numbers with no matches (0 to 9999ºF)

edit, I can email the spreadsheet to anyone interested, or post it online.

edit2. also checked negative, to -9999ºF, no matches

Bill, were you looking for reverse matches?
Direct matches could easily be done by adding a third column subtracting the first column from the second column. All the zeros are matches.
Finding reverse matches is a bit more difficult. I’m stumped for a formula. Anybody?

I loked for reverse matches. I used excel commands LEFT, RIGHT and MID to break the F number down to individual digits, then recombined them in reverse order via the CONCANTENATE command. Then compared the reversed F value to the C value via the IF command.

Only needed to check every 9 F values for obvious reasons.

you can download the spreadsheet at

EDIT: found an error, had to use the VALUE command to convert the reversed number, which is in text format, to an actual number. Still no matches.

A tip of the hat to your ingenuity, Bill :grinning:!

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