## Does a bag of holding burst if brought into the space created by Rope Trick?

A bag of holding has a special caveat:

Placing a bag of holding inside an extradimensional space created by a Handy Haversack, Portable Hole, or similar item instantly destroys both items and opens a gate to the Astral Plane.

Now, the 2nd level spell Rope Trick says:

(…) At the upper end of the rope, an invisible entrance opens to an extradimensional space that lasts until the spell ends.

The extradimensional space can be reached by climbing to the top of the rope. (…)

Is it safe to bring a bag of holding inside the rope trick extradimensional space?

## Is the Exclusive trick the only “official” way to keep others from using Handle Animal on a animal?

I’m asking this because I think it’s ridiculous to be able to handle someone else’s loyal animal (e.g. a guard dog, animal companion) without training the animal to accept such handling.

Exclusive (DC 20): The animal takes directions only from the handler who taught it this trick. If an animal has both the exclusive and serve tricks, it takes directions only from the handler that taught it the exclusive trick and those creatures indicated by the trainer’s serve command. An animal with the exclusive trick does not take trick commands from others even if it is friendly or helpful toward them (such as through the result of a charm animal spell), though this does not prevent it from being controlled by other enchantment spells (such as dominate animal), and the animal still otherwise acts as a friendly or helpful creature when applicable. (Animal Archive, p. 9)

I really hope there is another way, besides the seeming need for a trick like Exclusive. Otherwise it seems you could always use Handle Animal on someone’s else’s animal, even a opponent’s in combat! Wouldn’t all the domesticated animals in a campaign world need this trick?

By “official” I mean any officially licensed material from WotC for D&D 3rd edition & 3.5 or any Paizo published Pathfinder products.

## Would it be possible to launch an ambush from a rope trick?

I am currently a fairly new player who’s throwing their innocent Wizard into the maw of the beast. As I am still learning and getting used to the rules and tactical play I would like to confirm a few things about the Rope Trick spell.

The Rope Trick spell states the following:

(…) The rope can be pulled into the space, making the rope disappear from view outside the space. Attacks and spells can’t cross through the entrance into or out of the extradimensional space, but those inside can see out of it as if through a 3-foot-by-5-foot window centered on the rope. (…)

To me it sounds like these two conditions make it possible for a party hiding inside of the rope trick to ambush an unsuspecting patrol passing under the rope trick.

Also Falling mentions:

(…) At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.

For this tactic I have made a few assumptions:

• If the rope trick is less than 10 feet high the party can avoid fall damage.
• Dropping down and attacking can be done simultaneously.
• The party will gain a surprise round upon execution.

Aside from these assumption I also failed to find any information on Plunging Attacks. So I would like to know if this even a thing at all (to let our Barbarian and Druid look extra cool in return for assisting me in my madness).

## Gelfand’s trick (Gelfand’s lemma) in positive characteristic?

I came across this preprint that claims in Lemma 1.1 that Gelfand’s trick (also known as Gelfand’s lemma) only works in characteristic zero:

Let $$H < G$$ be finite groups. Suppose we have an anti-involution $$\sigma : G \rightarrow G$$ that preserves all H double-cosets. Then over algebraically closed fields of characteristic zero (G, H) is a Gelfand pair.

It is not obvious to me where the characteristic of the ground field being zero is used in the proofs from Lang’s $$SL_2(\mathbb{R})$$ book (Theorem 1 and Theorem 3 in Chapter IV), the introduction in this preprint, the last slides in these slides, or anything else that I’ve seen.

What causes Gelfand’s trick to fail in positive characteristic? In this setting, the groups are finite but I would also like to know the answer for the more general versions of Gelfand’s trick (i.e. also for locally compact groups with compact subgroups or even reductive groups over local fields with closed subgroups).

## Is there any practical trick to mentally count in Gray code?

When I was fairly young, I taught myself to count in binary. I thought it would be a fun party trick to impress people. I soon found out that it was not.

Over the years I’ve come to appreciate Gray code/reflected binary code for its property of only flipping one bit for each increment/decrement of the underlying count. But I’ve always been bothered by the fact that, if I wanted to mentally take any arbitrary Gray code and add or subtract 1 from it, I’d have to either convert it to and then back from its numeric value, or construct a table to work out what the next code should be.

It seems to me that there should be some trick that a person with “average” short term memory and addition skills should be able to do to take any arbitrary value in Gray code and figure out which bit to flip to get the next value… But I’ve never found it.

Does such a thing exist?

## Can Wifi probe requests be abused to trick clients into connecting to a fake AP?

I just read about WiFi probe requests and that it is possible to track clients by the MAC-Address in the request.

I was wondering if it would be possible to set up a malicious AP which responds “Yes, that’s me” to every probe request from clients, resulting in clients automatically connecting to that “known” network. A malicious AP could for example sniff the traffic from smartphones of people walking by whose devices automatically connected. Is that possible in theory?

## What is the trick behind the code?

def inc_subseqs(s): """Assuming that S is a list, return a nested list of all subsequences of S (a list of lists) for which the elements of the subsequence are strictly nondecreasing. The subsequences can appear in any order.  >>> seqs = inc_subseqs([1, 3, 2]) >>> sorted(seqs) [[], [1], [1, 2], [1, 3], [2], [3]] >>> inc_subseqs([]) [[]] >>> seqs2 = inc_subseqs([1, 1, 2]) >>> sorted(seqs2) [[], [1], [1], [1, 1], [1, 1, 2], [1, 2], [1, 2], [2]]""" def subseq_helper(s, prev):     if not s:         return [[]]     elif s[0] < prev:         return subseq_helper(s[1:], prev)     else:         a = subseq_helper(s[1:], s[0])         b = subseq_helper(s[1:], prev)         return insert_into_all(s[0], a) + b return subseq_helper(s, 0) 

I’m having trouble getting the idea of this function. Why prev is set to 0 at the begining, and what’s the functionality of a and b.I’m new to programming, please help!

## Probability of X being a trick coin (heads every time) after heads is flipped k amount of times

A magician has 24 fair coins, and 1 trick coin that flips heads every time.

Someone robs the magician of one of his coins, and flips it $$k$$ times to check if it’s the trick coin.

A) What is the probability that the coin the robber has is the trick coin, given that it flips heads all $$k$$ times?

B) What is the smallest number of times they need to flip the coin to believe there is at least a 90% chance they have the trick coin, given that it flips heads on each of the flips?

Here is my approach:

Let $$T$$ be the probability that the robber has the trick coin

Let $$H$$ be the probability the robber flips a heads k times in a row

$$Pr(T) = 1/25$$

$$Pr(H|T) = 1$$

$$Pr(T’) = 24/25$$

$$Pr(H|T’) = 1/2$$ when $$k=1$$, $$1/4$$ when $$k=2$$, $$1/8$$ when $$k=3$$… etc

$$Pr(T|H) = (1 * 1/2) / (1 * 1/2 + Pr(H|T’) * 24/25) = 1/13, 1/7, 1/4,…$$ etc

So the Pr(T|H) answer changes for every k, do I answer with the formula? How can I answer A? How do I make a probability distribution when k can be infinite?

Also is B 8 flips? Since when k = 8, Pr(T|H) = 1/256.

Thanks for any help.

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