Was Jesus crucified on Passover, or the day before? John vs Mark

The passages

And the first day of unleavened bread, when they killed the passover, his disciples said unto him, Where wilt thou that we go and prepare that thou mayest eat the passover?

Mark 14:12

Then led they Jesus from Caiaphas unto the hall of judgment: and it was early; and they themselves went not into the judgment hall, lest they should be defiled; but that they might eat the passover.

John 18:28

And it was the preparation of the passover, and about the sixth hour: and he saith unto the Jews, Behold your King!

John 19:14

The problem

In Mark, Matthew and Luke the disciples prepare a Passover meal, Jesus eats it with them on the evening that begins the 15th of Nisan, and he is crucified the next day. In John, the Last Supper takes place before the Passover (13:1), and the Jewish leaders have not yet eaten the Passover when Jesus is taken to Pilate. Jesus dies at the hour the lambs are being killed. The two chronologies cannot both be literal.

What believers and scholars say

Different calendars. Some propose that Jesus and his disciples followed a different calendar than the Temple authorities, perhaps one like that used at Qumran, which would let both meals be called the Passover. The evidence for this is suggestive but hard to confirm.

"Passover" can mean the whole festival. In John 18:28 "eat the passover" might refer to the festival meals of the following days, not the lamb eaten the night before. Defenders of the Synoptic dating prefer this.

John's theological timing. Many scholars think John deliberately shifted the day so that Jesus dies as the true Passover lamb (compare John 1:29 and 19:36). Others think the Synoptics have made the Last Supper into a Passover for liturgical reasons. Meier, after weighing the evidence, leans toward John's date.

Where this leaves it

The disagreement is clear in the text and has produced serious, unresolved scholarship. A calendar difference is a real option. So is the possibility that one Gospel adjusted the date to fit its message. Nothing in the surviving sources forces a choice, and most of the plausible answers cost something.