## Google Optimize for A/B test: Trying to edit existing HTML but says it’s over the limit even when I test deleting some of it?

I am trying to set up an A/B test of a company’s website for my project. There are certain changes I’d like to make such as changing the ‘favourites’ products on the home page to one with the top selling products which I was trying to do by substituting the existing code simply with the top selling products instead (i.e. their jpg, their links, their names etc).

However I found that when making ANY change (by selecting the element and clicking ‘edit HTML’), even testing it by deleting one character from the original code, that it then pops up with this error notification saying that it’s over the word limit. Even when I put the character back for example, the error message is still there. And it will say weirdly that it is quite a lot of the word limit even though it’s basically the original code! I then have to click cancel every time.

Please see the attached photo for reference (where I deleted one character from the original code to demonstrate how any editing (even deletion of original working code) then comes up with the error that the html is over the limit).

View post on imgur.com

Thanks in advance!

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## Splitting balls over sized bins

This is strongly related to Splitting a set of integers over a set of bins, but a much simpler case.

If we have $$N$$ indistinguishable balls and $$k$$ arbitrarily large distinguishable bins, we know the number of ways to distribute the balls over the bins (allowing for empty bins) is given by a binomial coeffcient

``binCounts[balls_, bins_] :=   Binomial[balls + bins - 1, balls]; ``

and if we want the actual splits, those are given by taking all permutations of integer partitions of $$N$$ of length $$k$$

``binSplits[balls_, bins_] :=   Apply[    Join,    Permutations[PadRight[#, bins]] & /@     IntegerPartitions[balls, bins]    ]; ``

Just to show this indeed works

``Table[    Length[binSplits[n, k]] == binCounts[n, k],    {n, 1, 20},    {k, 1, 10}    ] // Flatten // Apply[And]  True ``

This breaks down, though, when we have sized bins, i.e. each of our $$k$$ bins has some max number of allowed balls $$c_i$$. From this math.SE question I’m not expecting there to be a nice closed-form solution for the number of partitions. That doesn’t mean we can’t write an algorithm to generate them.

The naive approach would be to just filter our prior list of solutions

``binSplitsSized[balls_, binSizes_] :=  Block[{bins = Length[binSizes], splits},   splits = Apply[     Join,     Permutations[PadRight[#, bins]] & /@      IntegerPartitions[balls, bins]     ];   Select[splits, Min[binSizes - #] >= 0 &]   ]  binSplitsSized[10, ConstantArray[3, 5]]  {{3, 3, 3, 1, 0}, {3, 3, 3, 0, 1}, {3, 3, 1, 3, 0}, {3, 3, 1, 0, 3}, {3, 3, 0,    3, 1}, {3, 3, 0, 1, 3}, {3, 1, 3, 3, 0}, {3, 1, 3, 0, 3}, {3, 1, 0, 3, 3}, {3,    0, 3, 3, 1}, {3, 0, 3, 1, 3}, {3, 0, 1, 3, 3}, {1, 3, 3, 3, 0}, {1, 3, 3, 0,    3}, {1, 3, 0, 3, 3}, {1, 0, 3, 3, 3}, {0, 3, 3, 3, 1}, {0, 3, 3, 1, 3}, {0, 3,    1, 3, 3}, {0, 1, 3, 3, 3}, {3, 3, 2, 2, 0}, {3, 3, 2, 0, 2}, {3, 3, 0, 2,    2}, {3, 2, 3, 2, 0}, {3, 2, 3, 0, 2}, {3, 2, 2, 3, 0}, {3, 2, 2, 0, 3}, {3, 2,    0, 3, 2}, {3, 2, 0, 2, 3}, {3, 0, 3, 2, 2}, {3, 0, 2, 3, 2}, {3, 0, 2, 2,    3}, {2, 3, 3, 2, 0}, {2, 3, 3, 0, 2}, {2, 3, 2, 3, 0}, {2, 3, 2, 0, 3}, {2, 3,    0, 3, 2}, {2, 3, 0, 2, 3}, {2, 2, 3, 3, 0}, {2, 2, 3, 0, 3}, {2, 2, 0, 3,    3}, {2, 0, 3, 3, 2}, {2, 0, 3, 2, 3}, {2, 0, 2, 3, 3}, {0, 3, 3, 2, 2}, {0, 3,    2, 3, 2}, {0, 3, 2, 2, 3}, {0, 2, 3, 3, 2}, {0, 2, 3, 2, 3}, {0, 2, 2, 3,    3}, {3, 3, 2, 1, 1}, {3, 3, 1, 2, 1}, {3, 3, 1, 1, 2}, {3, 2, 3, 1, 1}, {3, 2,    1, 3, 1}, {3, 2, 1, 1, 3}, {3, 1, 3, 2, 1}, {3, 1, 3, 1, 2}, {3, 1, 2, 3,    1}, {3, 1, 2, 1, 3}, {3, 1, 1, 3, 2}, {3, 1, 1, 2, 3}, {2, 3, 3, 1, 1}, {2, 3,    1, 3, 1}, {2, 3, 1, 1, 3}, {2, 1, 3, 3, 1}, {2, 1, 3, 1, 3}, {2, 1, 1, 3,    3}, {1, 3, 3, 2, 1}, {1, 3, 3, 1, 2}, {1, 3, 2, 3, 1}, {1, 3, 2, 1, 3}, {1, 3,    1, 3, 2}, {1, 3, 1, 2, 3}, {1, 2, 3, 3, 1}, {1, 2, 3, 1, 3}, {1, 2, 1, 3,    3}, {1, 1, 3, 3, 2}, {1, 1, 3, 2, 3}, {1, 1, 2, 3, 3}, {3, 2, 2, 2, 1}, {3, 2,    2, 1, 2}, {3, 2, 1, 2, 2}, {3, 1, 2, 2, 2}, {2, 3, 2, 2, 1}, {2, 3, 2, 1,    2}, {2, 3, 1, 2, 2}, {2, 2, 3, 2, 1}, {2, 2, 3, 1, 2}, {2, 2, 2, 3, 1}, {2, 2,    2, 1, 3}, {2, 2, 1, 3, 2}, {2, 2, 1, 2, 3}, {2, 1, 3, 2, 2}, {2, 1, 2, 3,    2}, {2, 1, 2, 2, 3}, {1, 3, 2, 2, 2}, {1, 2, 3, 2, 2}, {1, 2, 2, 3, 2}, {1, 2,    2, 2, 3}, {2, 2, 2, 2, 2}} ``

but if the number of bins or balls get even moderately large, this quickly becomes unworkable, since we’re generating the entire `Binomial[balls + bins - 1, balls]` solution set.

So how can we do better? The easiest initial approach is to just filter our `IntegerPartitions` off the bat to exclude any unworkable solutions

``binSplitsSized2[balls_, binSizes_] :=  Block[{bins = Length[binSizes], max = Max[binSizes], splits},   splits = Apply[     Join,     Permutations[PadRight[#, bins]] & /@            Select[IntegerPartitions[balls, bins], Max[#] <= max &]     ];   Select[splits, Min[binSizes - #] >= 0 &]   ] ``

and this can give a significant boost

``binSplitsSized[10, ConstantArray[3, 5]] // Length // RepeatedTiming  {0.0018, 101}  binSplitsSized2[10, ConstantArray[3, 5]] // Length // RepeatedTiming  {0.00022, 101} ``

but can also be very easily stymied

``binSplitsSized[10, ConstantArray[10, 1]~Join~ConstantArray[1, 4]] //    Length // RepeatedTiming  {0.0019, 16}  binSplitsSized2[10, ConstantArray[10, 1]~Join~ConstantArray[1, 4]] //    Length // RepeatedTiming  {0.0018, 16} ``

So what good approaches are there do better?

## Does Warding Bond carry over damage type?

The warding bond spell description states:

While the target is within 60 feet of you, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, you take the same amount of damage.

If you cast the spell on another creature and then that creature is damaged, what type is the damage you take? If the target receives 12 slashing damage, do you get 6 slashing damage, or just 6 (untyped) damage?

## Where does a creature – flying low over a large body of water – descend when subject to the Earthbind spell?

In looking at the question Can the Erupting Earth spell be cast somewhere that isn’t on “ground”? other examples of spells involving the "ground" could be useful. Or not. Which lead to the question, where does a creature – flying low over a large body of water – descend when subject to the Earthbind spell?

According to the description of Earthbind:

An airborne creature affected by this spell safely descends at 60 feet per round until it reaches the ground or the spell ends. (XGtE pg 155)

Assuming the creature began its turn 60 feet above the water and failed its Strength saving throw, would the spell end:

a) when the creature reaches the water’s surface after 1 round (in other words, is the surface of the water "ground"?), or

b) would the creature continue to descend for the remaining 9 rounds for as much as 540 feet to the earthen bottom of the body of water (see note below), or

c) would the spell fail altogether, or

d) would the creature be forced essentially sideways for the duration of the spell, towards the nearest point of land, or

e) other?

Note re being forced towards bottom of large body of water:

Given a creature with 10 Constitution, 30 ft movement, and no innate swimming speed, its movement in the ocean would be 30 ft using both its Movement and Action to "Dash" (or 20 ft in difficult terrain).

540 ft of total movement would take 18 rounds (27 rounds in difficult terrain) and the creature – assuming it can’t breathe underwater or teleport in some fashion – would be unable to hold its breath after 10 rounds and would drop to 0 hit points after the next round.

’cause if the surface of the ocean is ground, guess what might . . . erupt?

## Grease spell: Can a creature with 10 strength or more jump over the greased area?

The spell Grease does the following:

Slick grease covers the ground in a 10-foot square centered on a point within range and turns it into difficult terrain for the duration. A creature that enters the area or ends its turn there must also succeed on a Dexterity saving throw or fall prone.

Since the affected area is only 10-foot long, can a creature with 10 or more Strength jump over the greased area, thus avoiding both the Dexterity saving throw and the difficult terrain?

For reference, the rules for Long Jump are the following:

When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump.

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