Recently, somebody told: "My grandfather was born on the first sunday of the year. His seventh birthday was also on a sunday!" In which year was this grandfather born?

Usually a date shifts by one day every year. So if for example 29 march is on a sunday, next year it will be on a monday. But if the next year is a leap-year, the date shifts by two days, in the example 29 march becomes a tuesday.

In seven years we expect at least one leap-year so after seven years you never can get the same day for the same date. But 1900 was not a leap-year (like all other years which are divisible by 100, except for the ones which are divisible by 400). Hence grandfather was born around 1900, in 1897 (because here the 7-year period is possible). More exactly he was born on January 3, 1897.