How many humanoids fit in a 10′ square when NOT in combat?

A typical humanoid, in combat, tends to occupy a 5′ square. Whilst brandishing sharp &/or dangerous weapons this just makes sense. Rules change for squeeze situations, pending relationship(s) – be they friend, foe, romantic (thus both), necessity (neither) or ‘strictly business’. These ‘combat &/or squeeze’ rules are somewhat realistic, makes intuitive sense and work well for in-game rulings.

Contrast this with reality:

Real world humans do not tend to observe nor respect one another’s boundaries. See any concert, crowded elevator, zombie movies – or try to enforce social distancing in most retail locations – you will observe very different situations.


Why This Is Relevant To D&D & To ALL ‘Role-Playing’ Gaming:

  • Seven goblins in a snowfall, backed up to a tiny bluff. Whilst huddling up to a tiny fire they are hit by bon-firing / cantripping that hits a large number of them.

  • Whilst thirty-three zombies cluster-reach through a portcullis a large urn of oil (above) pours & splashes down and is set ablaze.

  • Three clumsy ogres slip-fall into a 10′ cube-pit and seek to angrily push-throw one another out.

  • A blue dragon (lightning: ‘long and narrow’) breathing on the crush of two phalanx groups clashing – how many are shocked?

Related:

What is squeezing? – this defines what is in the 5e rules on squeezing during combat, including more squishy shapes, oozes and such.

Can medium creatures squeeze into smaller spaces? – this rehashes the rules quite well, including what a squeeze does to combat tactics.

What minimal space can a creature go through whilst squeezing? – this one requests information how much space a single creature (usually medium humanoid) needs. This also seems to suggest that i will also not find an answer for this ‘how tight is a group’ question.


Question Repeated: What rules exist in any edition to tabulate density of crowded groups in tight, pressing, forced or out-of-combat situations?

Note to editor: I searched Stack Exchange and found the above three previous questions / if i have missed this please accept my apologies. Also, any ruling from any roleplaying book, even if not 5e, could be excellent – i am encouraging any answer at this time. A good answer might even be from people who run concerts, dances or any other crowded pre-COVID events that – any that manage flows of moving-standing persons. Any guide would help. I may have to repost this in a different section of Stack Exchange or even (shudder), Reddit.

Is Exit (no square brackets) equivalent to Quit[] for refreshing the Kernel from within an Evaluation Notebook?

I prefer to use Exit as it conveniently requires fewer key presses over Quit[]. But before I use it regularly I need to know if there any subtle differences between Quit[] and Exit. The Wolfram documentation pages for Quit and Exit appear to be very similar and even call these two functions synonymous but I just need to be sure.

Thanks.

What is the point of origin for a square area of effect?

The spellcasting rules for areas of effect state:

A spell’s description specifies its area of effect, which typically has one of five different shapes: cone, cube, cylinder, line, or sphere. Every area of effect has a point of origin, a location from which the spell’s energy erupts. The rules for each shape specify how you position its point of origin. Typically, a point of origin is a point in space, but some spells have an area whose origin is a creature or an object.

A spell’s effect expands in straight lines from the point of origin. If no unblocked straight line extends from the point of origin to a location within the area of effect, that location isn’t included in the spell’s area. To block one of these imaginary lines, an obstruction must provide total cover.

Notably, square is not one of the shapes defined, yet there exist several spells which have a square area of effect, such as entangle or Evard’s black tentacles.

The spell grease tells us in its description:

Slick grease covers the ground in a 10-foot square centered on a point within range.

But this clarification is not present in the descriptions of entangle and Evard’s black tentacles.

So what is the point of origin of a square area of effect when it is not specified in the spell description?

When playing on a grid, can I pour a flask of oil on any adjacent square or just on the one I am standing on?

The description of a flask of oil says:

You can also pour a flask of oil on the ground to cover a 5-foot-square area, provided that the surface is level.

When playing on a grid, can I pour a flask of oil on any adjacent square or just on the one I am standing on?

Divide first n square numbers 1^2, 2^2, ……. n^2 into two groups such that absolute difference of the sum of the two groups is minimum [closed]

lets say Given input is n = 6 (n is as large as 100000) My task is to divide {1, 4, 9, 16, 25, 36} into two groups and PRINT these two groups

Possible Solution 1: dividing groups as {1, 9, 36} and {4, 16, 25} which gives abs diff as abs(46 – 45) = 1. So the minimum difference is 1 and the two groups are {1, 9, 36} and {4, 16, 25}

Possible Solution 2: Another Possible Solution is dividing groups as {9, 36} and {1, 4, 16, 25} which gives abs diff as abs(45 – 46) = 1. So the minimum difference is 1 and the two groups are {9, 36} and {1, 4, 16, 25}.

If there are multiple solutions we can print any one. Iam trying to solve it using https://www.geeksforgeeks.org/divide-1-n-two-groups-minimum-sum-difference/ but its not working.

I know that min difference is always 0 or 1 for n >= 6 but how to divide them into two groups.

And can we extend this problem to cubes, fourth powers, so on. if so what is the strategy used

To “rescue” a fallen ally, do you have to enter their 5′ square? [duplicate]

Apologies if this has been answered elsewhere, but I did spend a couple of hours researching this online and didn’t find anything definitve. I DM a campaign in which a party member has fallen unconscious and is about to start making death save rolls the following turn. A character (with flying in this particular example) wants to drag the ally out of the fray and then up to the roof for safety (they are fighting in a small open courtyard). I have seen a lot of opinion on the use of grappling for ally extraction as well as the action and movement economies to answer those related questions. However, right now I need to determine whether the rescuer will provoke an attack of opportunity when they extract the ally. Really, to me, it has come down to whether you are dragging an ally from your own square (and not within 5 feet of an enemy) or whether you have to enter their square in order to drag them.

Does carry vs drag change your answer? Does the ability to fly change your answer?

Expression involving square roots not simplifying

I have a relatively simple expression here that is not simplifying:

$ $ \frac{2 s_0 \left(\sqrt{\gamma ^5 s_0}+\sqrt{\gamma ^9 s_0}\right)+\sqrt{\gamma ^3 s_0}+2 \sqrt{\gamma ^7 s_0}+\sqrt{\gamma ^{11} s_0}+\sqrt{\gamma ^7 s_0^5}}{\gamma \left(\gamma ^2+\gamma s_0+1\right){}^2} $ $

$  Assumptions = {(s0 | \[Gamma]) \[Element] Reals, \[Gamma] > 0,     s0 > 0}; (Sqrt[s0 \[Gamma]^3] + 2 Sqrt[s0 \[Gamma]^7] + Sqrt[s0^5 \[Gamma]^7] +    Sqrt[s0 \[Gamma]^11] +    2 s0 (Sqrt[s0 \[Gamma]^5] + Sqrt[s0 \[Gamma]^9]))/(\[Gamma] (1 +      s0 \[Gamma] + \[Gamma]^2)^2) // Simplify (Sqrt[s0 \[Gamma]^3] + 2 Sqrt[s0 \[Gamma]^7] + Sqrt[s0^5 \[Gamma]^7] +     Sqrt[s0 \[Gamma]^11] +     2 s0 (Sqrt[s0 \[Gamma]^5] + Sqrt[s0 \[Gamma]^9]))/(\[Gamma] (1 +       s0 \[Gamma] + \[Gamma]^2)^2) == Sqrt[s0 \[Gamma]] // Simplify 

The output is:

(Sqrt[s0 \[Gamma]^3] + 2 Sqrt[s0 \[Gamma]^7] + Sqrt[  s0^5 \[Gamma]^7] + Sqrt[s0 \[Gamma]^11] +   2 s0 (Sqrt[s0 \[Gamma]^5] + Sqrt[s0 \[Gamma]^9]))/(\[Gamma] (1 +     s0 \[Gamma] + \[Gamma]^2)^2) True 

Why is Mathematica not simplifying to this much simpler form $ \sqrt{s_0 \gamma}$ , I think my assumptions should be enough. I can do the simplification by hand