Can a Stealth check ever be made passively?

The PHB, at p. 175, presents passive skill checks as a means to represent two different kinds of in-game scenarios:

Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster….

(Emphasis mine.) Notably, the entire section on passive checks is general and agnostic as to any particular skill. It does not say these skills can be used passively, but not those. The implication, it would seem, is that any skill can potentially be used passively in the right circumstance.

For the detection-type skills — Perception, Insight, and Investigation — passive checks are so common and well-documented that I don’t feel a need to cite sources for support. Other skills don’t lend themselves as readily to passive checks, but it’s at least conceivable to use them that way. For example, one could imagine using Passive Medicine to represent a character in a field hospital repeatedly diagnosing and treating injuries among troops at war, or using Passive History to represent a character’s spontaneous recall of a particular fact without the player first asking “Does my character know any relevant history here?”

Is there any use-case for Passive Stealth? Or do the rules on hiding and detection (see PHB p. 177) essentially require that all Stealth checks be active?

Has this (c-k)^n formula ever been seen before? [on hold]

I am Edward Solomon, and in my research into prime numbers and the Andrica Conjecture I geometrically derived a formula concerning the interior sum of partitions inside a rectangular rank-n tenor, which coincidentally made a striking statement equivalent to Fermat’s Last Theorem.

I really need to know know if this formula has already been discovered.

Here is the formula :

Let c be an integer, c must be odd. Let a be an integer, such that a < c. Let k = c – a, k > 1

$ 0 = \sum^{j=k-2}_{j = 0} (-1)^j\binom{k-2}{j}(c-2-j)^n $


EDIT

You can adjust c,k and n as you desire. Some posters have shown there are bounds on n, but that seems to be it so far (n < k-2).

From the above equation it follows that:   $ (c-k)^n = |\sum^{j=k-3}_{j = 0} (-1)^j\binom{k-2}{j}(c-2-j)^n|$

Several direct tests show it to be reliable: Let c = 89, let k = 9, let n = 4, the result is (80)^4, as predicted. c = 31, k = 20, n =3, the result is (11)^3 = (31-20)^3, again as predicted by the formula.

Geometrically this states that a n-cube of side-length (c-k) , is the alternating (k-2) binomial sum of first (k-3) n-cubes (of the same power) greater than itself.

From the above formula, we can make two statements (since Andrew Wiles already proved Fermat’s Last Theorem):

1: Given c, and let n = 2, then there exists only one of pair of integers, (k1, k2), such that their sum (when inputted into the formula) = c^2, if there exists any solution at all.

2:  Given c, and let n > 2, then there exists no solutions, (k1, k2), such that their sum (when inputted into the formula) = c^n.

How we would even proceed to prove these statements (without Wiles, 1995)…I have no idea! (well I do have ideas, since I know how to disprove a more generalized version involving rank-n tensors when all the dimensions of a n-rectangular prism are distinct prime numbers, but I do not see how to bridge the gap from a rectangular tensor to a cubic tensor, and furthermore why the case of n = 2 permits solutions for cubic tensors when the general case involving rectangular tensors does not).

Personally, what I find most interesting is that there even exists solutions when n = 2, since the method I used to derive that formula would suggest otherwise. For instance, test the Pythagorean Triple {39, 80, 89}, (k1 = 50, k2 = 9). It’s hard to believe that some expression containing 47 = (k1-3) binomial expansions, when added to another expression containing only 6 = (k2-3) binomial expansions, can somehow add up to square, especially if you saw the geometry of the implied processes in live action. 

I derived this result from my work on the Andrica Conjecture, Totatives and the counting of prime gaps by manipulating rank-n tensors (n be the size of the sieving set of primes) with prime number dimensions (n-dimensional rectangular prisms). If wish to see this work let me know, thankfully all of the information pertaining to Fermat’s Last Theorem occurs in the first chapter of my book. 

To make a long story short, I was confronted with having to count the number of viable systems of congruences that permitted coprime gaps (gaps between consecutive totatives) of certain lengths to occur, and the geometry involved in the manipulation of the tensors (the rank of the tensor is determined by the number of primes in the sieving set) containing the solutions  which yielded a rather large collection of simple formulas, since Chinese Remainder Theorem demands that every viable system of congruences exists within the tensor, and exists uniquely (making the geometry and counting rather trivial).

I myself do not have time to currently research this topic any further (at least alone), as I am devoted to finishing my work on the Andrica and Cramer Conjectures. So, citizens of the world, unite!

If you notice something interesting I’ll be glad to hear and forward you Chapter 1, Appendix A, Appendix B and Appendix F from my book on the Andrica Conjecture, as Chapter 1 contains all things related to Fermat’s Last Theorem.

Sincerely, Edward Solomon

P.S.

I apologize if these formulas were already known. I however cannot see how one could have derived them, other than by accident while working on something else (as I did haha).

P.S.2  Also be warned that I have submitted a formal paper on prime numbers and the Andrica Conjecture containing some of these observations, and have sent the same to several of my friend’s and colleagues, so do not attempt to use this work without giving me credit. You can use it without my permission…it’s public, but give me credit for deriving this monstrous formula. Thank you!

can i ever regain my lost bitcoins?

Even if you don’t know Bitcoin from blockchain, it’s likely you’ve heard something about cryptocurrencies. Also known as virtual currencies, digital assets such as Bitcoin, Ether and hundreds more are a hot commodity in online trading, and it’s possible for a smart investor to make a big profit. But the prospect of quick riches can blind some people to the risks and enable crooks to lure them into scams.

What is cryptocurrency? According to the U.S. Commodity Futures Trading Commission (CFTC), it’s a digital representation of value that isn’t backed by any government or central bank. Even so, this virtual money can be used to make purchases, and it can be exchanged for U.S. dollars or other conventional currencies.

But unlike government-backed money, a virtual currency’s value is driven entirely by supply and demand. That can create wild swings that produce big gains for investors, or big losses. And cryptocurrency investments are subject to far less regulatory protection than traditional financial products like stocks, bonds and mutual funds. (The CFTC does oversee virtual currency options and futures contracts, because it considers digital money to be a tradable commodity. The Securities and Exchange Commission has called for applying securities law to cover cryptocurrency exchanges.)

For all virtual currency’s high-tech gloss, many of the related scams are just newfangled versions of classic frauds. The CFTC has warned about “pump and dump” scammers who use messaging apps and chat rooms to plant rumors that a famous business mogul is pouring millions of dollars into a certain digital currency, or that a major retailer, bank or credit card company is going to partner with it. Once they’ve lured investors to buy and driven up the price, the scammers sell their stake and the currency plummets in value.

recently a friend was involved in this scam, he invested 50000USD after been convinced to do so in a certain commodity only for it to dip after doing so, it was his life savings, i suggested a certain global capital retriever to him, through the process of assets mapping, they effectively and successfully initiate chargebacks by leveraging the intelligence that we have collected on the company and the company bank accounts. hopefully this helps someone out there that has already been scammed, theres still a silver linning their skype contact is Gcapitalretriever and electronic mail is Gcapitalretriever @ outlook . com

When (if ever) should links be opened in a new window?

I have seen a lot of discussion on this topic but it all seems to be opinion based without any research backing up the assumptions.

It seems that there are times that it is particularly relevant to open links in new windows (providing help or interrupting processes) but what about the more ambiguous actions (i.e. links to external sites)?

Does anyone know of any (preferably recent) research on the affect links opening new windows has on users?

Has an optional “browser upgrade” message ever worked?

From time to time, we feel the urge to encourage users to upgrade their browser, especially IE. And from time to time, we’ve rolled out features that attempt to send this message to users, usually “lightbox” dialogs, but sometimes as banners, begging the user to upgrade.

But nothing works. If the dialog has a “close” button, users immediately click it. If it has a “cancel” link, however small and unobtrusive, users find it and use it, even if the link says “continue at your own risk.” And if it’s a banner, they just ignore it, not even bothering to click a button to close the banner.

(Obviously, we could just block certain old browser versions completely, but that’s an extreme choice that we wouldn’t want to do to more than a few percent of our visitors.)

It’s easy to brainstorm more/different ways to send this message (and there are a number of cute open-source projects to display an “upgrade browser” warning), but I’m wondering: has anyone ever rolled out a “browser upgrade” dialog that actually worked?

By that I mean, does there exist any documented case on any website where the data showed that rolling out a “please upgrade” message was followed by a sharp measurable drop in old-browser traffic?

Or even a reasonably large percentage of users actually click on a “Download” link in the dialog/banner to upgrade their browser?

EDIT: Folks around here can get prickly about proving causation, so I want to clarify: I’m not asking for data that “proves” that a banner caused users to upgrade. All I’m asking for is a documented example where somebody installed a “please upgrade” banner and observed that their old IE usage decreased shortly afterwards.

(Proving causation is hard, but if no one has ever even observed a correlation, that’s a surprising and important discovery.)