There is no problem at all. I believe Jesus was crucified on N15 and I also believe the scriptures testify to that account. Allow me to explain.
There are clearly 2 parts to the Passover Event and they occur on 2 separate Jewish Calendar Days. Go back to the original Passover in Egypt (Ex 12). The first part is the Passover Meal (eating of the slaughtered lamb) that occurs at twilight on N14. The second part is the actual Passover (God passing over the firstborns of Israel and striking down the firstborns of Egypt) which occurs on N15. The Passover lamb is eaten on the eve of the actual Passover as N14 transitions to N15.
Scripture is very clear N15 is the day the Israelite captives are led free from Egypt. God tells them they will observe the Feast of Unleavened Bread on that day (N15) because that was the day they were brought out of Egypt (Ex 12:17; Lev 23:6).
In the time of Jesus, scripture states Jesus is alive on the day of the Passover when they slaughtered the lambs, or N14. He then goes on to eat a meal with his disciples that night (Mark 14:12; Luke 22:7). He is arrested overnight (beginning N15) and crucified the following day (N15) during the sacred assembly that was required by the law (Ex 12:16; Lev 23:7).
N15 was a sabbath in which they were to hold a sacred assembly and they could also prepare food. It was also the Friday preparation day for the Saturday sabbath on N16, a sabbath in which they could not prepare food because it was a day of strict rest.
It is tempting to want to believe that Jesus MUST have died on N14, just as the passover lamb did, because Jesus is the Lamb of God. However, there are a few problems with that reasoning.
1- Jesus died at 3pm. According to the law, the passover lamb was supposed to be slain at twilight. Jesus claims he came to fulfill the law, so if Jesus were going to die in the same manner as the passover lamb, shouldn't he have died at twilight? (Matt 5:17) Some historical references suggest the passover lambs were being slaughtered between noon and 3pm on N14, and that could very well be true, but Jesus didn't die that day. He ate the Lord's supper that evening.
2- Jesus didn't come to die the death of the passover lamb; Jesus came to die OUR death. He is the propitiation of our sins, not the propitiation for the passover lamb. (1 John 2:2). In the original Passover, on what day were the firstborns of the Israelites supposed to die? N15. But when God saw the blood of the lambs, He passed them by. The death penalty was still due. Animal sacrifices don't atone for sins. (Heb 10:4) On N15, the day Jesus died, the firstborn of all of creation (Col 1:15) took the death penalty for us on the cross and became the Lamb of God. A final sacrifice once for all (Rom 6:10; 1 Pet 3:18)
The biggest source of confusion then is how Jesus could have died on a Friday, rise on a Sunday, and count that lapse of time as 3 days and 3 nights? That is what this article explains.
A review of the week that led up to the Passover would look something like this:
N10: Sunday (lambs chosen for slaughter); Triumphal Entry (Palm Sunday)
N14: Thursday (lambs slaughtered); Passover Meal Eaten/Lord's supper eaten
N15: Friday (sacred assembly & Feast Day) Jesus crucified in Front of the Crowd
N16: Saturday; High Day Sabbath
N17: Sunday; Resurrection Day
N14 is the day of the Lord's supper because Jesus obediently observed the Passover. He even says he had eagerly desired to eat it with his disciples (Luke 22:15). In this meal, Jesus offers his body and his blood to be eaten as the new covenant. In the original Passover meal, it wasn't enough to just slaughter the lamb but it also had to be eaten (Ex 12:8). The night transitioned from the 14th to the 15th and he is arrested and dies at 3pm on N15: the day the firstborns were to die.