yes you do need the longshot to get across the quicksand for the spirit temple( you could always just get the longshot and leave) my question is do you even need the tunics to complete the game. in the fire temple only when you teleport and some rooms across hyrule are the only times when you need it. and in the water temple you could always go fast to avoid drowning
i though there were some eye switches in the fire temple, and you have to beat the forest first. am i wrong? i really dont remember
o and spirit temple can be 3, 4, or 5. you need the bow to get to the water temple and you need the longshot to get to the spirit temple so its possible the spirit temple could actually be third. and it can obviously be 4 or 5
possible combinations.forest, fire, water, spirit, shadow.---------forest, fire, water, shadow, spirit-------------forest, water, fire, spirit, shadow----------forest, water, fire, shadow, spirit.------------forest, water, spirit, fire, shadow---------fire, forest, water, shadow, spirit,----------fire forest water spirit shadow---------fire forest water shadow spirit. im pretty sure these are all the combinations.
I know for certain that the zora tunic is entirely skippable/optional. I generally warp straight from the iron boots room to the Water temple and bypass it. Since your time under water or in death mountain/ in a hot place is 8* amount of hearts (i.e. if you have 5.5 of 6 heart containers full of health you get 44 seconds) you have plenty of time to do all the underwater parts of the Water temple with at least 8 heart containers or so. As for the Goron tunic I personally beat OOT 3D's regular quest without equipping it. I did acquire it because I didn't try to see if you could get to the Fire temple from the top entrance of death mountain into the crater but it could be possible. I think you can also carry bottled fairies to increase your time you can stay under adverse conditions, but I did the Fire temple with 18 heart containers since you can do Spirit before it. The only scary part is Volvagia but he's beatable in about a minute so the Goron tunic is unnecessary.
Also I came up with the same orders (no glitches or entering dungeons for items) you did, but you double counted fire forest water shadow spirit so there are 7 possible.
I just realized Mases wanted to include the Ice Cavern and Bottom of the Well in the discussion as well. The Ice Cavern must be done before the Water Temple but can be done as soon as you become adult link, and the Bottom of the Well can be done anytime after the Forest Temple but to add to the complexity of the issue it doesn't actually have to be completed or even entered since the lens of truth is optional. So adding the ice cavern to my 7 orders a few posts up creates 18 orders including the ice cavern but not the bottom of the well.
For Example: IC, For, Fir, Wat, Sha, Spi ; For, IC, Fir, Wat, Sha, Spi ; For, Fir, IC, Wat, Sha, Spi .... etc. So when there are 2 dungeons before water that creates 3 orders and only 2 orders are created when only forest precedes water for a total of 18.
Adding in the Bottom of the Well: there are 5 spots to do it after forest when forest is first (which is in 5 of the 7 orders) and 4 spots to it after forest when forest is second (other two).
5X5=25
2X4=8
=33
That leaves us with 18+33=51, but we also have to account for when the two minidungeons are completed in the same place between temples which creates another order
Example: For, Fir, IC, BotW, Wat, Sha, Spi OR For, Fir, BotW, IC, Wat, Sha, Spi
Doing this creates 9 more possible orders.
So without glitches or entering dungeons to gain the item and leave, OOT 3D can be completed in 60 different orders.
On a related note, if you want to consider the ability to grab a dungeon item and leave (like grabbing the bow then doing the Water temple first) in this discussion, there are 18 base temple orders (the only temple rules are Forest before Spirit and Forest, Fire, Water before Shadow). Adding the 2 minidungeons creates 137 orders, and considering grabbing bombs to do Jabu Jabu as the 2nd child link dungeon creates 274 orders without glitches. But with all the math I did, I'm probably mistaken.