Explanation

Anadyr (in Chukotka, Russia) and Nome (in Alaska, USA) are geographically very close to each other, separated only by the Bering Strait — a distance of just a few kilometers. However, despite their proximity, they lie on opposite sides of the International Date Line (IDL).

The International Date Line (IDL) is an imaginary line running roughly along the 180° longitude, where the calendar date changes by one full day when crossed. Travelling westward across the IDL adds a day, while travelling eastward subtracts a day.

Statement I is correct. Although Anadyr and Nome may show the same clock time — say, 8:00 AM — they are on opposite sides of the IDL, meaning the calendar date is different in both cities simultaneously. If it is Monday morning in Anadyr, it is Sunday morning in Nome. This is why people waking up for breakfast at the same moment in these two nearby cities are technically living on different days — a direct consequence of the IDL passing between them.

Statement II is incorrect. The statement claims that when it is Monday in Anadyr, it is Tuesday in Nome — this is factually wrong. Since Russia lies west of the IDL, Anadyr is ahead of Nome by one day, not behind. Therefore, when it is Monday in Anadyr, it is Sunday in Nome — Nome lags behind Anadyr, not the other way around. The direction of the date difference matters critically here.

Therefore, only Statement I is correct.