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Puzzler Answer (Fahrenheit to Celcius)

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

Sorry - wrong forum