The following is from Pope Benedict’s Holy Thursday 2007 sermon from L’Osservatore 4/11/07 issue.
…There is an apparent discrepancy in the Evangelists’ accounts, between John’s Gospel on the one hand, and what on the other Mathew, Mark and Luke tell us.
According to John, Jesus died on the Cross at the very moment when the Passover lambs were being sacrificed in the temple. The death of Jesus and the sacrifice of the lambs coincided. However, this means that He must have died the day before Easter and could not, therefore, have celebrated the Passover meal in person–this , at any rate, is how it appears.
According to the three Synoptic Gospels, the Last Supper of Jesus was instead a Passover meal into whose traditional form He integrated the innovation of the gift of His Body and Blood.
**This contradiction seemed unsolvable until a few years ago. ** The majority of exegetes were of the opinion that John was reluctant to tell us the true historical date of Jesus’ death, but rather chose a symbolic date to highlight the deeper truth: Jesus is the new true Lamb who poured out His Blood for us all.
In the meantime, **the discovery of the [Dead Sea] Scrolls at Qumran has led us to a possible and convincing solution ** which, although is not yet accepted by everyone, is a highly plausible hypotheses. We can now say that John’s account is historically precise.
Jesus truly shed His blood on the eve of Easter at the time of the immolation of the lambs.
In all likelihood, however, he celebrated the Passover with his disciples in accordance with the Qumran calendar, hence, at least one day earlier; He celebrated it without a lamb, like the Qumran community which did not recognize Herod’s temple and was waiting for the new temple.
Consequently, Jesus celebrated the Passover without a lamb–no, not without a lamb: instead of the lamb He gave Himself, His Body and His Blood. Thus, he anticipated his death in a manner consistent with his words: “No one takes [my life] from me, but I lay it down of my own accord” (Jn 10:18).
(Bolding done by me.)