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An ice day is a day on which the maximum temperature doesn't exceed 0 °C and a tropical night is a night on which the minimum temperature exceeds 20 °C. Probably no part of the tropics has experienced an ice day and most continental locations far north haven't experienced a tropical night. My guess is that a location that has experienced neither would have to be coastal or an island in the mid-latitudes: Eureka, California, is one example (the coldest day was 1°C and the warmest night 17 °C). Campbell island (NZ) and Tristan Da Cunha might also be examples, but I couldn't find exact data to prove it.

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    $\begingroup$ You'd have to define "never" - in recorded history? Since the formation of the earth? $\endgroup$
    – Eonema
    Commented Feb 16, 2023 at 17:46
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    $\begingroup$ you might want to update your kowledge about tropical nights in the arctic. $\endgroup$ Commented Feb 17, 2023 at 15:09
  • $\begingroup$ Seems a reasonable question to me (other than the "never")... basically the answer should be: very maritime locales near continually modest water temperatures? Because you're only allowing for about 25°C range over the course of the year. $\endgroup$ Commented Feb 18, 2023 at 2:11
  • $\begingroup$ Never was imprecise. Let's go with never recorded in modern times (for example, since 1850). $\endgroup$
    – user28506
    Commented Feb 28, 2023 at 18:47
  • $\begingroup$ @trondhansen it's conjecture of course, but even in the country we originate from tropical nights are rare. I would say it's unlikely that places like Tynset and Karasjok have ever had one. $\endgroup$
    – user28506
    Commented Feb 28, 2023 at 18:58

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