Total distance per day for different travel paces?

The travel pace description and table on page 181-182 of the Player’s Handbook states that a normal travel day may contain 8 hours, and gives the following table:

 Pace:   /Hour    /Day         Miles in an 8-hour walking day:   Fast   4 miles  30 miles --> 4x8 = 32 miles (-2 miles a day) Normal   3 miles  24 miles --> 3x8 = 24 miles (OK)   Slow   2 miles  18 miles --> 2x8 = 16 miles (+2 miles a day) 

Why is there an difference of 2 miles for fast and slow pace?

In Ghost Ops do NPCs get free attacks only on total Bullet Time failure or also on partial failure?

I have the original version of Ghost Ops (which uses Fudge dice), not the Savage Worlds version or the OSR version. This question is about that original version, but if you think the rules in one of the other versions can throw some light on this, please chip in.

On page 132 of the core rulebook there is an example of a failed Bullet Time action. The PC was attempting to shoot 3 NPCs in the head, and needed an 8 but only got a 6.

The book then has some more rules:

The Handler can decide that the Operator succeeded in some of the attempt. Maybe they barged the door and managed to get 2 of the attempted headshots off but missed the third. Failing a Bullet Time event places the Operator as prone for 1 round, allowing any Tangos free attacks. Deciding to attempt Bullet Time is risky but can be ultimately rewarding.

So, if the GM has said the failed roll can be partial success (hit 2 of the NPCs) and partial failure (miss the 3rd NPC), which of these applies?

  1. It still counts as a normal fail – the PC is prone and subject to a free attack by all three NPCs (assuming the two he shot aren’t dead or disabled).
  2. It still counts as a ‘reduced’ fail – the PC is prone but only the third NPC, who was not hit, gets a free attack.
  3. It counts as a success – the PC is not prone and the NPC/s don’t get free attacks.
  4. The GM decides on a case by case basis.

I’m hoping there is clarification for this question in one of the expansions, or in an updated version of the pdf (I only have a print copy). I’ve failed to find any errata on the internet.

Total catastrophic failure, or should a GM ever allow re-rolls and do-overs?

It’s a critical moment in the game at the end of a marathon session, everyone is on the edge of their seats, and the player rolls… a 1. Evil bad guy wins, party dies, game over. As a GM, what should you do? Probably don’t structure your game to hinge on the result of a single roll, right? Well what if it was an improbable-but-possible series of bad rolls?

Should you ever let people re-roll after failing? I’m thinking no, otherwise everybody will want to re-roll after every bad outcome.

What about letting the party start over from when they first entered the room? Just for the sake of convenience and without any sort of time reversal game mechanic.

How to deal with the total differential of implicit function equation

I want to find the total differential of $ z=z(x, y)$ , $ z=z(x, y)$ satisfies the implicit function equation $ (x+1) z-y^{2}=x^{2} f(x-z, y)$ (function $ f(u, v)$ is differentiable).

Dt[(x + 1) z[x, y] - y^2 == x^2*f[x - z[x, y], y], z[x, y]] 

But the above result is not in the form of $ \mathrm{d} z=p(\mathrm{x}, \mathrm{y},\mathrm{z(x,y)}) \mathrm{d} \mathrm{x}+\mathrm{q}(\mathrm{x}, \mathrm{y},\mathrm{z(x,y)}) \mathrm{d} \mathrm{y}$ .

What should I do to get the form I want?

Test examples:

$ \left.\boldsymbol{d} z\right|_{(0,1)}=-\boldsymbol{d} x+2 \boldsymbol{d} y$

Sleep’s hp total and (half-) elf targets

Situation: A Gnome Bard sits in a prison cell, next to her in another cell sits a half-elf Ranger. There is one guard with them in the room, with two or three more in the next room. The Bard casts Sleep at a point that includes everyone but her.

My understanding of what happens: Half-elves are not immune to the spell Sleep, as the spell ignores only unconscious, undead, and immune-to-being-charmed creatures, of which half-elves are neither. Therefore, if the half-elf has sufficiently low hp to be affected, his current hp is deducted from the spell’s remaining roll total before moving to the next target, but he does not fall asleep due to Fey Ancestry. This means that including any targets with Fey Ancestry in the area of a Sleep spell is just a waste of the spell’s potential.

Question: Is my understanding of the situation correct? I’m not as much asking whether or not the half-elf should be affected, as I’m quite sure he should be, but more whether or not his hp would be deducted from the spell’s roll.

Relevant PH fragments: (emphasis mine)

Fey Ancestry. You have advantage on saving throws against being charmed, and magic can’t put you to sleep. (PH p.39)

Sleep (…) Creatures within 20 feet of a point you choose within range are affected in ascending order of their current hit points (ignoring unconscious creatures). Starting with the creature that has the lowest current hit points,(…) Subtract each creature’s hit points from the total before moving on to the creature with the next lowest hit points. A creature’s hit points must be equal to or less than the remaining total for that creature to be affected. Undead and creatures immune to being charmed aren’t affected by this spell. (PH p.276)

How to Find Total number of Possible Concurrent Schedules in Transactions?

My friend come up with this idea:- Let T be the total number of transactions, the Total number of possible schedules will be (n + m + k)! /( n! m! k!). While the number of concurrent schedules will be ((n + m + k)!/ (n! m! k!) – T!) .

Question:- Consider 3 transactions T1,T2 and T3 having 2,3 and 4 operations respectively. Find the number of concurrent schedules?

My Answer:- Total no. of concurrent schedules = 9C2 * 7C3 * 4C4 = 1260.

I want to know my friend is correct or me ? should we also count serial schedules in concurrent schedules ? or Something else ? Please clear my doubt !!!!!!!!!!

Is minimising the total number of one entries in binary matrices $CA$ and $C^TB$ NP-HARD?

Given a two rectangular binary matrices $ A$ and $ B$ with dimensions $ c\times a$ and $ c \times b$ respectively, does there exist an invertible binary matrix C with dimensions $ c \times c$ such that the total number of 1 entries in $ CA$ and $ C^TB$ is below a target threshold $ t$ ?

Here we are working in $ GF(2)$ , where multiplication and addition are AND and XOR respectively.

What is the hardness of this problem? Are there approximation algorithms to this problem?

We know this problem is in $ NP$ , as a valid $ C$ can be used as a certificate. Also, we know how to find $ C$ when there exists the a solution for $ t = a+b$ , by using Gaussian Elimination.

Add Total Row To PIVOT Query

I want to add a TOTAL monthly row to my query, below is my DDL, how can I have an additional row, under the last employeename that is labeled TOTAL and it shows the SUM() of the sales for ALL employees for that month?

Create Table #empSales (     employeename varchar(100)     ,saleamt decimal(10,2)     ,saleMonth varchar(100) )  Insert Into #empSales VALUES ('James', '1.00', 'January') ,('Richard', '3.28', 'January') ,('Barb', '4.13', 'January')   Select  employeeName ,SUM(January) As JanAMt ,SUM(February) As FebAMt ,SUM(March) As MarAMt ,SUM(April) As AprAMt ,SUM(May) As MayAMt ,SUM(June) As JunAMt ,SUM(July) As JulAMt ,SUM(August) As AugAMt ,SUM(September) As SepAMt ,SUM(October) As OctAMt ,SUM(November) As NovAMt ,SUM(December) As DecAMt FROM #empSales PIVOT (      SUM(saleAmt) For saleMonth IN (January, February, March, April, May, June, July, August, September, October, November, December) ) As pvt GROUP BY employeeName Order By employeeName