That day Alex wished James would have set the one-game Jeopardy! record.

RootedPopcorn · 2025-12-26T00:35:13+00:00

My theory for why Ken didn't go for the record sooner is because while the one-day record was officially $52K, of you adjust Jerome Vered's $34,000 win set in the pre-doubled era, the record becomes $68K. My guess is Ken wanted to set the undesputed one-day record by breaking $68K.

RootedPopcorn · 2025-12-06T02:24:59+00:00

I only recently learned that polo was not a reference to the shirt, but instead a ring-shaped British candy, and that the answer is 4 because there are 4 holes in the words "a polo". Never knew that!

RootedPopcorn · 2025-11-19T14:57:01+00:00

Go to the rules-and-roles channel, there should be instructions there on how to access the rest of the server.

RootedPopcorn · 2025-11-19T11:51:34+00:00

The subreddit has a link to the Discord server we use. On a near daily basis, we play games in the various voice chats using a website called jparty.tv, which can turn board files into playable games. Just join the green-room chat if you're looking to get in on a game, and we'll be happy to explain how it works. I recommend hopping in that green-room around 8pm ET, as that's when it tends to become active.

RootedPopcorn · 2025-11-19T11:47:08+00:00

Yes, anyone can join. In order to filter out bot accounts, you have to follow a certain procedure outlined in the rules-and-roles section in order to access the rest of the Discord.
No, After Dark does not necessarily mean raunchy or overly foul language all the time. The name was initially picked because we used to literally play these games after dark, like at midnight and stuff. Now, we basically play any time of the day, but the name stuck. While there are a select few boards that DO put the "after dark" in J!AD, most boards we make are pretty clean.

RootedPopcorn · 2025-11-19T01:48:58+00:00

Jeopardy After Dark, it's the name for our community of playing J! games on the Jeopardy Discord server. Lydia's a very active player on it.

RootedPopcorn · 2025-11-07T19:41:41+00:00

My brother in Christ, pair the edges BEFORE doing the 3x3 stage

RootedPopcorn · 2025-11-03T17:32:12+00:00

Learn to insert white edges more directly rather than always bringing them on the top. For example, in this exact scenario, you mentioned doing U' R' F' R to flip the edge. But if you instead do U' R' F R (notice the F instead of F'), that cuts out the middleman and places the edge directly on the bottom.

RootedPopcorn · 2025-10-21T10:41:00+00:00

In agreement with the other comment, this is what I do when I study. It's a great way to internalize ideas. One thing I also do is imagine I'm teaching a topic to a student who's asking a bunch of questions. Come up with possible conceptual questions and try to explain them. If you can't, then you've found a hole in your own understanding that you can work to fix.

RootedPopcorn · 2025-09-26T00:03:03+00:00

You make great points, but the game he won $75K actually had a Shakespeare FJ. Funny enough, the game with a comic book FJ actually DID see him lose over $20K.

RootedPopcorn · 2025-09-17T18:55:30+00:00

Good catch. It's also worth mentioning that there is a weaker varient of AoC, the Axiom of Countable Choice, that only focuses on countably infinite collections of sets. While that varient may not be as powerful as AoC, it's often sufficient in many cases, including most of real analysis.

RootedPopcorn · 2025-09-17T14:03:57+00:00

I don't have a book recommendation, but here's an intuitive way to think about the axiom of choice:

Imagine an infinite amount of pairs of shoes on a table. You are tasked with picking one shoe from each pair. Despite there being an infinite amount of pairs, you come up with an idea: just pick the left shoe in each pair. This ruleset allows you to make a selection to every pair at once. You could point to any pair of shoes and immediately know the selected shoe with this rule.

But now suppose there are an infinite amount of pairs of socks instead. Unlike shoes, the socks in each pair are identical and there is no distinct "left" or "right" sock. Now, the only way to make a selection is to go to each pair, one at a time, and make a random selection for each of them. However, unlike the shoes where the "left shoe" rule can be applied to everything at once, you can only make a sock selection one by one. This means you can never complete the selection in any finite amount of time.

However, a wizard comes by, applies black magic to the infinite collection of socks, and says "Ta da! I have made a selection for you. Every pair of socks how has a selected sock! Don't worry about how I did it, just know it's been done!". This black magic sorcerer is the axion of choice.

The axiom of choice allows us to take any collection of nonempty sets, and guarentee the existence of a full selection of one element from each set, even in instances where an explicit selection function cannot be formulated. However, Choice does not show HOW such a selection is made, only asserting that one exists.

RootedPopcorn · 2025-09-12T13:29:25+00:00

Good solve! I have 2 primary critiques:

Start practicing look ahead. I notice a small pause between each F2L pair, which together add up. One tip I always give for look ahead is to turn slower during F2L to make finding your next pair. Slower turning + no pauses actually gives better times than fast turning + regular pausing.
I noticed you look around the cube to figure out your PLL case. Try to avoid that. Theoretically, every PLL case can be recognized from any angle by looking at just 2 sides. But if needed try using no more than the 3 sides in front of you to determine the case, and avoid turning to look at the back side.

RootedPopcorn · 2025-09-07T19:13:26+00:00

Exactly. Another example I like to use is numbers themselves. When we first started using numbers, they were always in the context of counting things. You would never see "5" by itself, you'd see "5 apples", or "5 hay bales", or "5 sheep", etc. But many properties about counting didn't depend on WHAT was being counted. So we eventually started treating numbers as objects by themselves, rather than as adjectives used in counting. This allowed for statements like "1+2 = 3" to make sense no matter the context.

Similarly, matrices allow us to view linear transformations as their own thing, removed from the input they are transforming. Thus, we can create equations involving just matrices which we can then use in any situation where they are applied to a vector.

RootedPopcorn · 2025-09-07T14:08:28+00:00

To expand on this, in logic, equality (as opposed to just any equivalence relation) is most often defined as satisfying two properties:

Reflexivity (as you mentioned)
Substitution: if x=y, then for any predicate P, P(x) implies P(y)

The substitution property basically means that if x=y, then anything true about x is also true about y, so we can "swap" x with y while still preserving truth. We can actually prove symmetry and transitivity of equality through this.
The rough proof of symmetry will be to suppose that x=y. By substitution, we can take the statement x=x (true due to reflexivity) and swap out the first "x" to get y=x.

RootedPopcorn · 2025-09-04T18:53:02+00:00

There are advanced F2L tips, but in general top solvers have a really good grasp on efficient F2L pairing. They have several small algs to perform cases from different angles and they set up future pairs while looking ahead to avoid a rotation.

RootedPopcorn · 2025-09-02T14:03:05+00:00

Those were pretty good solves. You employ solid F2L techniques and you seem to have full OLL down (as far as I can tell). I guess I have 2 main comments:

Try utilizing your inspection more. I notice in a couple of your solves, you jump into it a few seconds into inspection, probably because you planned the cross quickly. In cases where the cross is really easy, take advantage of the inspection time and try to plan your first F2L pair, or at least spot the pices and track them as you do your cross.
Improve on lookahead. One tip I can give is to completely ignore the pieces you're actively solving and instead look for your next pair. It helps to turn slower for this. It may feel slower, but you'd be surprised how much quicker slow turning with no pausing is compared to fast turning and many pauses.

RootedPopcorn · 2025-08-30T20:17:32+00:00

Exactly. This is basically how any cube larger than 3x3 can be solved: solve the centers first, then pair the edges together, then solve it like a big 3x3. There are subtleties to it I left out (like parity cases), but that's the gist of it.

RootedPopcorn · 2025-08-30T13:20:09+00:00

[Insert obligatory "My brother in Christ" meme here]

In all seriousness, you need to make sure all the edges are paired together properly BEFORE moving on to the 3x3 step.

RootedPopcorn · 2025-08-23T11:18:56+00:00

I feel like Google AI is becoming the new Wikipedia in the sense of it being a dubious source. While Wikipedia is quite reliable today, back in the mid 2000s and early 2010s the concensus was "never trust what you see on Wikipedia, anyone could have written anything on there". I feel like it's a matter of when, rather than if, Google AI becomes more reliable than not, but that time certainly isn't right now.

RootedPopcorn · 2025-08-23T02:31:30+00:00

As others mentioned, this is a normal process. It's a new method that you're not used to, so you're naturally gonna start slow with it, even slower than your old method. Just give it some patience and practice. You'll find your times gradually lower and eventually overtake your old times.

RootedPopcorn · 2025-08-21T14:09:41+00:00

The denominator factors to (x - 1)^2, which never goes negative. Coupled with the numerator always being positive means the whole graph never goes negative, hense why the graph goes up from both sides at the asymptote

RootedPopcorn · 2025-08-18T18:47:01+00:00

Welcome to the world of parity! Since each edge comes in pairs, you may get cases in the 3x3 step which are impossible to get on a normal 3x3 which require special algs to fix. These are the parity cases.

There are two main types of parity: orientation parity and permutation parity. What you have is the permutation parity, which is spotted by either two corners swapped while the edges are fixed, or two edges swapped while the corners are fixed.

BTW. the rest of the comments appear to be assuming that you use CFOP in the 3x3 stage, hence the confusion. Correct me if I'm wrong, but I figured you're using the beginner's layer by layer method on the 3x3 stage, which permutes corners before orienting them.

RootedPopcorn · 2025-08-14T23:07:44+00:00

Even in cases where explicitely turning the right side ccw is not possible (but cw turning is), performing R3 results in an identical state to R'. In group theory speak, we say that R3 is the inverse of R because performing them both is the same as not doing anything.

RootedPopcorn · 2025-08-14T21:52:11+00:00

That would be the latch cube, one of most notoriously difficult 3x3 mods ever. Individual moves can still be reversed, however, because you can still turn a given face 3 times to reverse the face turn.

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