In 1940, an unusual coincidence took place when Palm Sunday (which is one week prior to Easter Sunday) occurred on the same day as St Patrick's day. In Ireland, which has St Patrick as its patron saint, people were able to wear both the shamrock and the palm on the same day.

St Patrick's Day falls on March 17 but Easter Sunday, and hence Palm Sunday, moves according to the rules that determine Easter.

Easter Sunday falls on the first Sunday after the full moon occurring on, or after, the March equinox (taken as March 21). So for Palm Sunday and St Patrick's Day to be on the same day, March 17 must fall on a Sunday (on average 1 in 7 years) AND there must be a full moon on either March 21, 22, or 23. The interval between successive full moons is approximately 29.5 days and so the chance of a full moon on any of these three dates is 3 in 29.5. This makes the combined chance of both Palm Sunday and St Patrick's Day coinciding as approximately 1 in 69 years (a probability of 0.015 per year).

This is only a statistical (ie, average) estimate. So are we actually due for a repeat of this coincidence shortly? The answer is no because the next such occurrence is in the year 2391 - almost three hundred years from now. Beyond that there is another coincidence in the year 2475, making only two such occasions in 500 years, very much less frequent than the average expected.

But statistics always applies if we take a long enough view. For example, if we consider the next 5000 years then there will be 76 occasions when Palm Sunday and St Patrick's Day coincide. This is very close to the expected number of such events.

Material prepared by Richard Thompson