Does exploration movement rate in Basic D&D (B/X) include trap/secret-door detection?

In the Basic Rulebook for D&D, on page B19, it states that characters can move 120′ in a dungeon per turn (10 minutes). Later it states that this movement assumes players are mapping carefully, searching, and trying to be quiet.

What is meant by ‘searching’? Are characters automatically getting a detect trap and detect secret door roll (every 10′ or per trap/door) as part of this movement rate? It seems unclear what searching exactly means in this context.

How to build interesting exploration challenges for mid- to high-level characters?

As a DM, I feel like I have a pretty solid grasp on how to build interesting combat and social encounters for parties of any level. However, I often struggle to do the same for the exploration pillar of the same, especially at mid to high levels.

Note that this question is about the exploration pillar as described in the basic rules:

Exploration includes both the adventurers’ movement through the world and their interaction with objects and situations that require their attention. Exploration is the give-and-take of the players describing what they want their characters to do, and the Dungeon Master telling the players what happens as a result. On a large scale, that might involve the characters spending a day crossing a rolling plain or an hour making their way through caverns underground. On the smallest scale, it could mean one character pulling a lever in a dungeon room to see what happens.

The problem that I’m facing is that most exploration challenges I can think of such as deep chasms, poisonous swamps, lava streams, hidden treasures, et cetera are trivially defeated once the party has access to spells such as levitate, fly, locate object, create food and water, … Some of these spells are available at lower levels but there they actually take a significant investment of spell slots, which becomes less of an issue at higher levels. I do not want to take away these spells from the party, but that means many exploration challenges I put on fail to provide an actual challenge.

One possible way to answer this question would be to provide a list of what elements make up an interesting exploration challenge. For the combat pillar, these elements would be things like: interesting enemies, an interesting location, a clear objective that isn’t just ‘kill all enemies’, … Likewise, for social encounters these elements include the different factions involved as well as interesting personalities for NPCs, their objectives, secrets, flaws, … So my question is: what are the elements making up an interesting exploration challenge?

Tips on theater of the mind dungeon crawling/location exploration?

I’ve been struggling with making exploration of locations/dungeon crawls engaging for the players.

I’ve tried a few things:

  • "And then you enter another room with X, Y, and Z" provides no choices, even if stuff in the rooms is interesting.
  • "You see two doors ahead of you" provides no meaningful choices.
  • "You met an NPC who outlines areas of interest in the dungeon which are X, Y, and Z" provide some semblance of choice, but ultimately I’m not sure how to make choice matter.

I think I’m missing the core concept of what makes exploring a place fun.

What’s the best way to represent gradual memory loss/Amnesia in an exploration adventure?

I’m going to DM a D&D 5e hexcrawl Westmarch-style, and for story-wise reasons the worst danger the players will have to face is Amnesia.

Each character will have a 7th ability score called Memory as per the variant Honor/Sanity rule in the DMG, equal to 3d6 + their highest modifier between Int, Wis, or Cha.

This score will reduce over time for each day of travel, and can only be recovered by resting in certain checkpoints (for example their starting outpost).

Now, i did my research, and the options I thought to represent what happens when you lose Memory are:

  • They start losing Int/Wis/Cha at the rate of 1 point/hour, and once they reach 0 they’re lost until someone finds them again.

PRO is easier for me to manage
CON it sounds too much videogame-ish and doesn’t translate well in role-playing terms.

  • They start suffering level drain effects at the rate of 1 level/hour, and same as above, but this time no way to recover the character.

PRO easy to manage, I don’t remember where I found the rule about level drain but it just says to give characters -1 to hps and every roll until they recover those levels
CON same problems, moreover I don’t like the fact that it also affects physical characteristics as Constitution, something that isn’t quite “forgettable”.

  • I mess up the notes they’ve taken, and the map they’ve drawn, during the current exploration (as per the spell Modify Memory).

PRO The most interesting option from the roleplay perspective
CON Why their memory loss would affect physical records? And even if it did, my tampering would be easily identifiable.

  • I lie and give them false information about where and when they have been.

PRO Would be easy to spot the misdirections by using their notes, and avoid a TPK
CON Would be easy to spot the misdirections by using their notes, and avoid a TPK.

  • I write off something off their character sheet each time they completely lose memory.

Desperate times call for desperate measures.

Now, if I just wanted something they could roleplay I wouldn’t have asked, but since it’s an hexcrawl and exploration mechanics is something with a great weight, I need something that has a mechanical impact too.

What have I missed?
What I have not thought of?

Is there no “exploration speed” in DCC RPG?

DCC RPG distinguishes between ten-second rounds for combat, and ten-minute turns for exploration (p. 76), but seems to only give speeds for actions (p. 77) and for overland moment (p. 308), but appears to be missing “exploration speed” (or movement per turn) which is to be found in most OSR games (e.g. LotFP Rules & Magic, p. 38). Is this the case, or am I missing something?

Is the intention that you just count movement generally action-by-action, but then round up to a turn after combat? This would make dungeon exploration much faster in DCC RPG than in other old school games, and would also seem to make the idea of a ten-minute exploration turn somewhat redundant.

high school level math (calculus) exploration idea? IB

I would appreciate if you guys could help me out by giving me some possible topics (not too hard, high school level, possibly relating to calculus) that I could explore as part of my math investigation (also know as the IA in the IB program). I would need to write a 12 page paper on the topic and formulate a research question on it that somewhat relates to my life (although this is the thing that concerns me the least). I really like differential equations/ solids of revolution/ taylor series/ integrals but I am unsure on how I would apply these to my exploration and come up with a research question on them. Thank you so much for your help.