Nissan 20th as the crucifixion date is so far only my proposal, very controversial and rejected (so far)
This theory is based actually on the obstacles of the other two proposals: 14 and 15. If Jesus was not crucified on the 14 or the 15, then He was crucified some other date. It happens that reading the Pentateuch, the Passover fest was not restricted to the first day, but last a week long, being a lamb sacrificed every day. That makes possible – just possible – for Christ being the Lamb if crucified any date of that week long Passover. The point is that the only days that are preparation days are the 14th and the 20th. If is not the 14th, then is the 20th.
The problem with the 20th is that besides being a logical and smart solution, it seems not to have any support on the Gospels. But it has. The interpretation that Jesus was crucified the very same day of his arrest is traditional but is not what the Gospels say.
The Gospels recorded that Jesus was before the Sanhedrin by sunrise; and also he was before Pilates by sunrise. That makes at least two sunrises between the arrest and the crucifixion. The Gospels also states that Jesus was before Pilates by noon, and that Jesus was crucified by 9 AM. The only explanation is that Jesus was crucified next day morning after being at Pilates. Searching for more evidence I found that Peter did denied Jesus along two days.
Not only that. Paul says that Jesus kept appearing to the disciples for 40 days. That is the exact numbers of days between the Sunday after the 20th and Pentecost.
Also there are external evidence. The judicial system of the Roman Empire makes impossible for a man being crucified with a few hours trial. The same happens with the Jew judicial system. Both denies a crucifixion the same day of the arrest.
Additionally there is some practical problem. It is hard to have Jesus at the cross by 9 AM if he has to be trialed for Anas, Caiaphas, the Sanhedrin, Pilates, Herod, and Pilates again. Not only that, but the Gospels describe the trial at the Sanhedrin as way too long. And not to forget Jesus being presented to the multitude, and all the punishment that both the Jew and the Roman applied on Jesus. It is impossible for all that to happens in about three hours.