Since you get 5 keys instead of 1 after defeating the 4th and 6th bosses, you can actually complete the game with 39 keys. I also found a method to beat the Great Palace after 10 door entries. If you fall while against the right edge of the room, you'll transition to the room to the right of the one you're on.
Zelda II Discoveries!
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I made these discoveries years ago, but struggled to actually find a place to share them. These could potentially revolutionize the way people play Zelda II.
With the Fairy Glitch, it is thought the maximum number of times you can go through a door is 10, but it is possible to enter a door many more times. The trick is to cast FAIRY on the first possible frame after entering the door (which may only work on odd/even frames). You may have to cross out-of-bounds to get back to the door, which takes about 15 minutes. Also, if you enter a door 6 times, you can get multiple keys from the bosses of Palaces 4 and 6. You could also get the Magic Key early by entering the first door 6 times and the second door 3, then going to the cave near the "River Devil", scrolling the screen, heading back, and then entering New Kasuto's widest buliding,and going left to enter Kasuto. Then you can obtain the SPELL magic and use it to get the key early, without even using any keys if you have FAIRY to get the required items.