Enigma 1293: Reverse Fahrenheit
16 September 2014
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From New Scientist #2451, 12th June 2004 [link]
“Multiplying by 9/5 and adding 32,” I explained to my clever nephew George, “is useless in practice. What you need is some memorable equivalents, like 10 °C being 50 Fahrenheit. Here’s one I’ve invented: 16 °C = 61 °F. See, to get from one to the other you just reverse the two digits.”
“Actually 16 °C = 60.8 °F,” I said.
“So 61 is near enough,” I said.
“Near enough is not exactly right.”
“But you cannot do it exactly,” I objected sourly.
“You can’t, because you insist on boring old base 10. But I bet I can, using other bases,” George retorted. Off he went to investigate, and was soon back. “-90 °C = -130 °F,” he said, “and to base 21 this says -46 °C = -64 °F. I have other examples, including two between the freezing and boiling points of water.”
What were the two examples that George found? Give your answers in the form x °C = y °F where x and y are written in base 10 (and x lies between 0 and 100).
Note: I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The current estimate is that the line will be connected at the end of September 2014.