What is the most damage possible in a single round of combat?

The rules are:

  1. The character can be any level up to 20, any class, and any race, using any spell, weapon, ability, or item, provided they are all available in an officially released capacity (so no Unearthed Arcana).
  2. This character gets a single round to inflict damage. Movement, Action, and Bonus Action (if needed). No reaction.
  3. The character can be buffed prior to this turn with either their own or another character’s spells or abilities, again requiring these buffs to be available in an officially released capacity. For example, Haste and Bless on a Fighter is fine. Assume there are allied characters with these spells, items, or abilities to allow for these effects.
  4. Assume unlimited amount of turns to prep for this round in which you deal damage. You can buff as much as you want, or cast a spell that requires multiple rounds, just as long as the turn you actually deal damage is the final turn.
  5. The character is assumed to hit (if it is an attack), or the enemy is assumed to have failed their saving throw (if it is a DC effect such as a Fireball spell). Assume no damage resistance from the enemy.
  6. The character does max damage with their attack. A 1d12 greataxe would do 12 + STR. Fireball would do 48 instead of 8d6. Assume no criticals. For Rogues, assume Sneak Attack.
  7. No insta-kill spells or abilities. Power Word Kill technically doesn’t deal damage. It just lowers the HP to zero.
  8. You can include an additional round for any/all in-game companions, provided they are acquired via the character’s abilities, spells, or items. So a Ranger’s animal companion, a Wizards group of zombies from Animate Dead, and a Sorcerer’s familiar with Dragon’s Breath are fine. An NPC Knight that swore an oath to protect your character as a quest reward is not allowed. You can assume the same rules as above for the companions: they all hit and do max damage. You can assume these companions can have items equipped, provided that is legal in the SRD (so no giving your bear a sword).
  9. The only environmental effect you can consider is max fall damage: 20d6 for 120 damage. But your character has to cause the enemy to fall during their attack. For this purpose, you can assume the enemy is standing 5 ft from the edge of a cliff. Otherwise, assume you cannot setup or alter the environment in any way outside of spells. No setting up traps.
  10. Ignore effects like Wild Magic Surge or items that cast random spells, as they are too unpredictable for the purposes of this calculation.

For what applications of the traveling salesman problem, does visiting each city at most once truely matter?

Traditionally, the traveling salesman problem has you visit a city at least once and at most once.

However, if you were an actual traveling salesman, you would want the least cost route to visit each city at least once, and you wouldn’t be bothered visiting a city 2, 3, or more times. For given city, you might stop and hawk your wares only once, and on subsequent visits, only drive through the city without stopping.

Consider an undirected graph having a city incident to exactly two edges. The cost on one of these edges is only 10 units, while the cost on the other is 99,999,999,999. If you insist on visiting each city at most once, then you are forced to incur the cost of the high cost edge. However, if you allow yourself to visit cities multiple times, then you simply leave the way you came in (on the low cost edge). The low cost edge leads you back to a city you’ve passed through before.

The traveling salesman problem is highly contrived for an actual traveling salesman. I want to give students an application for which there’s a real incentive to visit each city at most once. For what applications is visiting each city a critical aspect of the problem?

Number of circuits with at most $m$ logic gates

I’m working on the same exercise as described in this post:

How to show that hard-to-compute Boolean functions exist?

In the answer there I don’t understand how the number of circuits with at most $ m$ gates was found to be $ O(m^{4m})$ . My construction of the number of gates required:

Let any logic gate in the circuit take 2 inputs, which could be any of the $ n$ inputs or any of the $ m-1$ other logic gates. Then there are $ {{m+n-1}\choose{2}}$ possibilities for the inputs into any logic gate. There are 16 different functions that act on 2 inputs, so let there be $ 16{{m+n-1}\choose{2}}$ possibilities for the inputs and type for any logic gate. Lastly, since there are $ m$ gates, there will be $ 16^m {{m+n-1}\choose{2}}^m$ possibilities for the entire circuit.

Now we can say $ {{m+n-1}\choose{2}}^m < \frac{1}{2^m}(m+n-1)^{2m} < \frac{1}{2^m}(2m)^{2m}$ when $ m = 2^n/\log n$ (or $ 2^n/n$ ), so $ 16^m {{m+n-1}\choose{2}}^m < (32m^2)^m$ . So we would want to show that $ (32m^2)^m$ is less than $ 2^{2^n}$ . This doesn’t seem to be true anywhere, so I must have made a mistake somewhere.

I’ve looked online a bit and have found three different sources say that the number of circuits with at most $ m$ inputs is $ m^2$ , $ 2^m$ , and something similar to what I came up with. I understand that which gates to use is vague, but these are fundamentally different functions, and I’m very confused.

What are the most recommended colors for the UI of a mobile app that is used under sunlight?

To use the app, users have to increase the brightness of the screen and this causes the battery to run out faster and still the best experience is not perceived.

It is an app that users use daily for 6 hours under sunlight taking meter readings located in the customers’ house.

They make a tour in the street visiting around 500 houses.

Why do most dashboards use capital words?

Most car manufacturers seem to use ALL CAPS for the interiors’s buttons and switches, at least when they are not using symbols. Example:

enter image description here

They even use capitals for things that are not even controls, like the indication where the AIRBAGs are in the car.

I thought that all caps where harder to read? (http://uxmovement.com/content/all-caps-hard-for-users-to-read/), so I am wondering: is there any specific reason for this?

How to get PIDs of processes with most network usage in descending order

I’m using my phone’s hotspot for using internet on my laptop with Ubuntu 18.04 installed. But even if I’m not doing anything, my laptop is still using the data and consumed my whole data pack within 20 minutes.

This is happening from last 3 days and I’m looking for a solution. I want to know what exactly is using this much data?

On Windows, network usage is directly visible in Task Manager. So, I guess there is an equivalent way to do the same on Linux.

I tried using ps command but I don’t think it gives details about network usage (Correct me if I’m wrong).

Also, I tried searching on stackoverflow and came across tools like iftop and many others. But I’m not able to find any details about the cause of the issue from any of the tools.

I’m not even able to install those tools mentioned on the articles found on the web/stackoverflow.

So, I want to know if there is any command that will sort the processes according to the network usage and that too without using any tools that need to be installed.

Is there any way to do this?