**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.

[enigma1293]

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This Python program runs in 34ms.

Solution:40°C = 104°F, 85°C = 185°F.The first works in base 17: 40 = 26

_{17}, 104 = 62_{17}.The second works in base 26: 85 = 37

_{26}, 185 = 73_{26}.