Tom and Ray said that there was no algebraic solution to this puzzler. But there is. Here is the condensed version:

Variable Description Domain

F1 Fahrenheit Temp: 10s digit integer

F2 Fahrenheit Temp: 1s digit integer (1,2)

F3 Fahrenheit Temp: Decimal [0,1)

C1 Celcius Temp: 10s digit integer (1,2)

C2 Celcius Temp: 1s digit integer

Identities

F = 10F1 + F2 + F3

C = 10
C1 + C2

F1 = C2

F2 = C1

F = 1.8C + 32

solve for F1

F1 = (17F2 - F3 + 32) / 8.2

F2 = 1

F1 = 5.97560975609756 --> 6

F2 = 2

F1 = 8.04878048780488 --> 8

check

F C

61 16

82 27

Well done, except that one of them (I don’t even try to keep them straight), the one who presents the Puzzler and doesn’t know when it’s time for Stump the Chump, not the one who forgets the Puzzler and presents Stump the Chump, said, specifically, “Now, I don’t know if there’s an algebraic way to solve it…” so your premise is wrong.

If only you had posted your solution before it was broadcast. My own thought was to look up the Modulo function, but I cheated and made a spreadsheet.

Well there’s an easy way and a hard way. Easy way, google temp conversion and look at the list of comparative temps. Couple minutes tops. Hard way, figuring out a formula.

Sorry - posted to the wrong forum. I have moved to “The Show”

@ZombieWoof - I guess you are right about “I don’t know if …” v “There isn’t”

@Bing - The easiest way is to set up a spreadsheet.

I used the easiest way possible. I waited for the answer. My math has been messed up since I did missile computer and radar repair in the Air Force. Hexadecimal computations have a way of changing your thinking about everyday math.