At the north pole, all the lines of longitude (and hence timezones) converge on a single point. So, if you are standing there what time is it? (I would assume that it is GMT since all the timezones are just + or – offsets, so when they converge only GMT is left. Alternatively it could be all times simultaneously).

More of a question is what time is it 100m south of the pole? Here the timezones are just over 25m apart, but since they are separate, is it logical to use them? Walking around the pole at this proximity certainly makes a mockery of time – take a holiday there, walk round the pole once a day and it will always be same date. So, how far north do you go before giving up on timekeeping?

Even Wikipedia seems non-committal on this one…

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