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Programming Enigma Puzzles
From New Scientist #2013, 20th January 1996 [link]
Within the Earth’s atmospheric range, it is not possible to convert any whole number of degrees Fahrenheit into Celsius by reversing the digits. There is a good approximation in the case of 82 °F, which is nearly 28 °C the same may be said for 61 °F and 16 °C, but in neither case is the conversion exact.
It is possible to construct another scale to Celsius, sharing zero as freezing point, but with a different boiling point, which is a whole number berween Celsius’s 100° and Fahrenheit’s 212°, so that there is a positive point on the Fahrenheit scale which may be converted exactly into the equivalent temperature on the alternative scale simply by reversing the two digits.
What is boiling point on the alternative scale, and what is the convertible Fahrenheit temperature?