How many feet of speed does 1 foot of movement cost under the following conditions?  To be clear, all are being suffered at once.  If anyone has a specific rules reference, please explain yourself!  Some numerical values above have multiple possible reasons for being your answer, so please also specify, if there's any ambiguity, how you got your answer - I did my best to guess why each answer might be popular, but I am very fallible.

1. Climbing, swimming, or crawling is +1 foot per foot.
2. Difficult terrain is +1 foot per foot.
   1. In case it matters, this can easily come from a spell, such as Ice Storm or Wall of Water.
3. Wall of Sand sets your cost to 3 feet per foot.
4. Transmute Rock sets your cost to 4 feet per foot.
   1. Note: Plant Growth also sets it to 4 feet per foot.  I am not including it in the poll because it's not a distinct number, but be aware it (and other effects like it) could theoretically be in play at the same time.

 EDIT:  If anyone knows how to edit the poll name after creation, I'd appreciate it.  "test" is an ugly name.  :'(

Any extra movement cost apply as indicated in the Being Prone or Climbing, Swimming, and Crawling in Difficult Terrain. So they should adds up.

Your Mileage May Vary. ☺

Being Prone: Every foot of movement while crawling costs 1 extra foot. Crawling 1 foot in difficult terrain, therefore, costs 3 feet of movement.

Climbing, Swimming, and Crawling: Each foot of movement costs 1 extra foot (2 extra feet in difficult terrain) when you’re climbing, swimming, or crawling. Y

I made my vote, but it is only my particular idea on the ruling (the “additional movement” penalties add, so 8’), so I hold no delusions  that it is the only way to rule. 

I'm not 100% sure what the question is TBH. It asks what the movement speed would be under the following conditions but then lists a bunch in an odd way. If you mean in an area that has every condition you link in the OP the answer is (1+(2-1)+(2-1)+(3-1)+(4-1)+(4-1))= 11 feet per foot.

But that isn't a poll option. And, you say Plant Growth isn't included, but don't really make any mention of what is included instead other than 'all'. But some of the remaining effects are mutually exclusive. You cannot be in two walls at the same time, for example. Nor can you be swimming or climbing across the soft muddy ground.

The only conclusion I can see where we can stack as many of these as possible while also ending in an available poll option is to be Crawling in Ice Strom through a Wall of Sand overtop ground affected by the Transmute Rock to Mud. If this was the case, then 8 feet per foot.

Quote from Ravnodaus>>

I'm not 100% sure what the question is TBH. It asks what the movement speed would be under the following conditions but then lists a bunch in an odd way. If you mean in an area that has every condition you link in the OP the answer is (1+(2-1)+(2-1)+(3-1)+(4-1)+(4-1))= 11 feet per foot.

*squints*  Ah, I think I've backsolved it.  You think the answer is 8.  Thanks!

But that isn't a poll option. And, you say Plant Growth isn't included, but don't really make any mention of what is included instead other than 'all'.

I covered this in the original post.  What is included is swim/crawl/climb, difficult terrain, wall of sand, and transmute rock.

But some of the remaining effects are mutually exclusive. You cannot be in two walls at the same time, for example. Nor can you be swimming or climbing across the soft muddy ground.

I'm not interested in which particular effects people assume to be mutually exclusive - the question is how to combine the effects when they aren't.  Restating the original post for clarity, that means the effects in play are 2 instances of +1 foot per foot, 1 instance of set foot per foot to 3, and 1 instance of set foot per foot to 4.

The only conclusion I can see where we can stack as many of these as possible while also ending in an available poll option is to be Crawling in Ice Strom through a Wall of Sand overtop ground affected by the Transmute Rock to Mud. If this was the case, then 8 feet per foot.

Yes, that makes consistent sense with your earlier reference to "11".  Your interpretation is that you convert all coercions to additive modifiers and then stack them like additive modifiers.  Assuming you didn't vote yet, then as of this post that brings us to:

• 2/9:  add all coercions and all additive modifiers (10)
  • I'm fascinated this got votes but 14 didn't, since both 10 and 14 here require you to interpret "coerce" as a different mathematical operation without converting the underlying number.  That is, we got votes for coerce(4) = add(4), but no votes for coerce(4) = *4.
  • Double-fascinating because this is the least consistent algorithm that got votes - coerce(4) isn't add(4) all the time (or else it would result in 5), but is interpreted as add(4) only when combined with a second coerce.  Again, coerce(4)=*4 got no votes, but is more consistent - coerce(4)=*4 means you get the same answer even when it's the only operation.
  • Makes 3 assumptions:
    • Coerce(X) + Coerce(Y) = X+Y when X>1 and Y>1
    • Coerce(X) + Coerce(Y) = max(X,Y) when X = 1 or Y = 1
    • Coerce(X) + 1 = X + 1, not Coerce(X+1)
• 4/9:  convert coercions to additive modifiers (e.g. coerce(3) is +2 and coerce(4) is +3) in the same way difficult terrain is implicitly converted by the rules, then add them and all additive modifiers (8)
  • The most mathematically consistent of the answers, because it makes exactly 1 assumption which matches how we know difficult terrain is handled, and then sticks to it.
  • That 1 assumption is "costs X foot per foot is really an additive modifier of +X-1".
  • As a formula, the 1 assumption:
    • Coerce(X) + Coerce(Y) = 1 + X-1 + Y-1 = X + Y - 1
    • Equivalently, Coerce(X) + 1 = Coerce(X+1) = X + 1
• 3/9:  take the largest coercion and add all additive modifiers to it (6)
  • Interestingly, despite votes for this, no-one voted for coercions beating additives by going second - this particular algorithm assumes you coerce before adding (since if you add first, you'll get 4 - add 1, add 1, coerce to 4).
  • Makes 2 assumptions:
    • Coerce(X) + Coerce(Y) = max(X,Y)
    • Coerce(X) + 1 = X + 1, not Coerce(X+1)

Reinterpreted:

• 9/9 players agree, in no uncertain terms, that the answer isn't 4, so it seems we (full disclosure: I didn't vote) all agree that whatever happens, it's harder to walk through a Wall of Sand or Transmute Rock/Plant Growth in Difficult Terrain than it is without Difficult Terrain. 
• However, only 6/9 agree that it's harder to walk through a Wall of Sand on top of Transmute Rock/Plant Growth - 3/9 think that while Difficult Terrain isn't lost in the noise of how difficult the other factors are, Wall of Sand is.  That's a full 2/3 to 1/3 disagreement.
• 9/9 players agree the answer isn't 14, so costing 3 foot per foot isn't multiplying by 3.  However, 2/9 think costing 3 foot per foot is sometimes adding 3 and sometimes isn't, depending on if there are other coercions.  4/9 think costing 3 is always adding 2, and 3/9 think it's not adding at all - you stack coercions by taking the strongest.

This is by definition not consensus, which means the answer is a solid "ask your DM".

Quote from quindraco >>

• However, only 6/9 agree that it's harder to walk through a Wall of Sand on top of Transmute Rock/Plant Growth - 3/9 think that while Difficult Terrain isn't lost in the noise of how difficult the other factors are, Wall of Sand is.  That's a full 2/3 to 1/3 disagreement.

This is by definition not consensus, which means the answer is a solid "ask your DM".

No one here thinks that difficult terrain should be ignored because your question stated that it shouldn't.

Difficult terrain very much might be ignored if it is inherently overridden by a spell: if the terrain is unstable rocks it is difficult but then you transmute it to mud then it is worse from the spell but has lost the +1 of the rocks. Same if you were in difficult terrain brambles and someone cast plant growth to make worse brambles. Difficult terrain already only applies when the DM decides it should and your post demands that it must for the purposes of the calculation.

Quote from RegentCorreon >>

Difficult terrain already only applies when the DM decides it should

I don't understand how this is material to the thread, but that's false.  Here are examples where the RAW simply states Difficult Terrain without DM intervention:

• Ice Storm, as mentioned in the original post
• Wall of Water, as mentioned in the original post.
• Spike Growth

Also, just to be clear (I'm not accusing you of saying anything about this, I just want to be clear for everyone's benefit on the question), a DM is naturally free to both a) inflict Difficult Terrain and let the rules resolve (which is what this thread is about) or b) inflict Difficult Terrain and force it to resolve, which is largely irrelevant to this thread - any DM can do anything they want at any time - except for any DMs in this thread who always force it to resolve (because I explicitly asked the community how they resolved it), which means it's up to that particular DM, not to me. 

So to be as clear as possible:  if you're a DM, you should be voting how you rule.  If you're not a DM, assume the Difficult Terrain has been inflicted by the rules but nothing else has been, and vote how you would expect a reasonable DM to rule/how you would petition the DM to rule.

I think the best RAW analogue would be armor class. You get one AC “calculation” (which seems to mean anything that says “your AC = x”); if you have multiple options, you pick one.

Likewise, if multiple effects say one foot of movement costs x feet of movement (as opposed to x additional feet), you (or, more likely, the DM) pick one. That’s the Occam’s razor way of handling it. Then, explicitly additive modifiers (a shield for AC, difficult terrain for movement) add to the base assignment.

Other solutions require, at best, making up more new rules than I care to for an extremely rare occurrence, and at worst, invalidating perfectly fine rules that already explicitly exist.

I voted for 8[1+1+2+3] since Wall of Sand and Transmute Rock are affecting two adjacent mediums, both of which the character has to navigate.

If the effects were physically overlapping, such as in the case of two air effects, then I would have the greatest impediment supersede any lesser impediments.

I agree with RegentCorreon (I think) that transmute rock would override "normal" difficult terrain, but that leaves me with an answer of 7 feet of movement per foot traveled (+3 for transmute rock, +2 for wall of sand, +1 for climbing or whatever)

Oh, I did my math wrong. I'd also be looking at 7 for the same reasons.

I went with 8, but I don't understand the bit in brackets:

Wall of Sand increases the cost by 2.

Transmute Rock increases the cost by 3.

Other two effects both increase the cost by 2.

Base cost of 1.

----

However, during the game I might go with simplicity and just add all the numbers together for a cost of 9.

3+4+1+1