Was Jesus Christ crucified on the 14th of Nisan (April 3, 33) or the 15th (April 4, 33)? The Jewish calendar calculates a day from sunset to sunset, thus the Last Supper (on the Thursday evening) and Jesus' crucifixion (on Friday afternoon) happened in the same day. In John Gospel this day was the 14th of Nisan (April 3, 33 CE) of the Jewish calendar; In the three Synoptic Gospels the Last Supper is a Passover meal so Jesus' crucifixion must have taken place during the afternoon of the festival itself, the 15th of Nisan (April 4, 33 CE). 

Both dates obviously can not be true. Which date is correct?
Writing in The Mystery Of The Last Supper, Professor Sir Colin Humphreys, a scientist at the University of Cambridge, proposes a new solution, based on a combination of Biblical, historical and astronomical research. He urgues that Jesus used a different calendar and crucifixion took place in the 14th of Nisan (April 3, 33 CE) of the official post-exilic Jewish calendar. He explains:

" I have worked with an expert astronomer to investigate, for the first time, the possibility that a third Jewish calendar was in use in the first century A.D. The official Jewish calendar at the time of Jesus' death was that still used by Jews today: a lunar system in which days run from sunset to sunset. This was developed during the Jewish exile in Babylon in the sixth century B.C. Before that, however, the Jews had a different system. This is referred to in the Book of Exodus, in the Old Testament, when God instructs Moses and Aaron to start their year at the time of the Exodus from Egypt.

There is extensive evidence that this original Jewish calendar survived to Jesus' time. It was used by groups such as the Samaritans, Zealots, some Galileans and some Essenes. Under this pre-exilic calendar, Passover always fell a few days earlier than in the official Jewish calendar, and the days were marked from sunrise to sunrise, not sunset to sunset.

Using our reconstruction of this calendar we can see that in A.D. 33, the year of the Crucifixion, the Passover meal was on the Wednesday of Holy Week. From the clues they give, it's clear that Matthew, Mark and Luke all used the pre-exilic calendar in their description of the Last Supper as a Passover meal, whereas John uses the official calendar in which the Last Supper was before the Passover.

Holy Thursday is the well-known day on which Christians annually commemorate the Last Supper of Jesus. But my research shows that we should really be celebrating this on the Wednesday of Holy Week. A Wednesday Last Supper with the Crucifixion on Friday also allows just the right amount of time for all the events the Gospels record between the Last Supper and the Crucifixion".