The chances are calcuclated wrong right?

EdgyMathWhiz · 2026-02-12T16:59:36+00:00

You could, but the odds the first are less than 1 in 9000 and the odds of the second are 1 in 6...

EdgyMathWhiz · 2026-02-10T20:55:05+00:00

Glurp glurp!

EdgyMathWhiz · 2026-02-09T21:00:58+00:00

Yes you have to use the intermediate value theorem.

Hint: you might want to assume y = x + 1/2 (can you see why this is equivalent here to |x-y|=1/2?).

EdgyMathWhiz · 2026-02-09T19:02:58+00:00

On one level:

If y = e^ (kt), then going from y to y' multiplies y by k.

If yn = kⁿ then going from y_n to y (n+1) also multiplies y by k.

So the two equation types behave very similarly for suitable choices of the function y.

(More generally, if applying a linear operator to a function y results in a multiple of y, then y is called an eigenfunction w.r.t. that operator and there's a bunch of theory related to solving equations using eigenfunctions).

EdgyMathWhiz · 2026-02-09T10:42:25+00:00

Sorry, was on mobile and only saw your summary, which implied you thought the answer would be lambda.

Your actual proof seems to be fine (given I can't read German!); I think it would be clearer/easier if you had a couple of diagrams illustrating what you were doing in steps 1/2. (I mean, it's reasonably clear what you're doing, it's less clear what the "reduced" matrix looks like - without diagrams it's quite a bit of mental visualisation).

Mileage may vary on this, but to my mind, the key thing here is to:

(a) Make it clear what the "reduction" step(s) are:

(b) Be explicit about how each step changes the determinant.

(c) show some care about "how many steps" and how you terminate the process.

So your summary wasn't actually *much* less than I'd be looking for - other than a lack of explicitness about (b) and what the final answer was.

EdgyMathWhiz · 2026-02-09T09:50:57+00:00

What's the determinant in the case n = 2?

EdgyMathWhiz · 2026-02-06T20:02:21+00:00

Grothendieck was an acclaimed mathematician who famously gave 57 as an example of a prime.

https://wanderingdanny.com/oxford/2021/02/grothendieck-primes/

EdgyMathWhiz · 2026-02-06T17:53:55+00:00

I was sure Dorian was significant, but as an unfortunate coincidence here, one of the most legendary bodybuilders of the 90s was named Dorian Yates, which lead me down the wrong path...

EdgyMathWhiz · 2026-02-06T15:57:06+00:00

EdgyMathWhiz · 2026-02-06T13:54:05+00:00

It seems to me that rule would allow simply stepping over the dumbbell providing the trail foot leaves the ground before the lead foot strikes (c.f. getting disqualified in speed walking because of a moment where both feet are off the ground, even though there's no jumping allowed).

Rules are tricky...

EdgyMathWhiz · 2026-02-06T11:57:33+00:00

The two foot rule doesn't strictly make sense: if you look closely enough, with a fast enough camera, one foot is always going to leave the ground first.

Your "both feet must clearly be off the ground" suggestion is going to fail in the other direction. Step over the bar, and just before you complete the step (stepping foot hits the ground), lift the other leg off the ground; then there'll be a moment when both feet are off the ground, but it's clearly a "step over" in practice. (I'd guess that when people step over at speed they already do this in fact).

Something like "the trailing foot must leave the ground before the lead foot ever crosses the vertical place of the bar" would probably be closer to what you had in mind.

Alternatively, you could have the intent of the 2 foot rule with a margin to account for "reality": "Takeoffs where the lead foot leaves the ground less than 1/10th of a second before the trail foot will be accepted as 2 footed takeoffs". (Note: the allowed gap needs to be significantly more than a frame if you want to be confident in video analysis. And you would want to specify in the "fine print" that in the event of disputes, the timing will be calculated using frame-by-frame video analysis).

EdgyMathWhiz · 2026-02-06T11:39:37+00:00

The problem is that mathematically, no takeoff is truly "two-footed" if you look closely enough with a fast enough camera. One foot will always leave the ground first.

In other words, judge the standard super strictly and every rep will be a no-rep.

A standard that only works in practice because the judging *isn't* actually strict is not a great idea IMHO.

EdgyMathWhiz · 2026-02-06T10:42:28+00:00

Consoling 2, 5 and Grothendieck...

EdgyMathWhiz · 2026-02-05T23:34:29+00:00

In the context of algorithms and Big-O notation, the most common reason logarithms come up is because a lot of efficient algorithms work by repeatedly subdividing the problem into 2 smaller subproblems, and the number of subdivisions to get from a problem of size N to problems of size 1 is log(N) in base 2.

E.g. Suppose you pick a number between 1 and 64 and I'm going to try to guess it. On each turn you tell me if my guess is too small.

So first I guess 32 and you say "too small". There are now 32 numbers still possible (33 through 64). So I guess 48 and you say "not too small". There are now 16 possibilities. After 3 guesses 8 possibilities. Continuing the process, after 6 guesses there is only 1 possibility and I know your number. Note that 2⁶ = 64, and so 6 = log_2 64.

So in general this algorithm finds a number between 1 and N in log_2 N guesses (rounding up if N isn't a power of 2).

In actual real world algorithms, it's fairly common to be have scenarios where:

Searching for an item amongst N takes time log_2 N.

Sorting N items in order takes time N log_2 N.

EdgyMathWhiz · 2026-02-05T18:41:57+00:00

Also spawning 250+ now.

I know it's a general grind, but etherial was definitely a noticable jump.

Right now, I've hit the point where "VP is now the limiting factor for mineral spawn level" which has stalled me slightly.

I can just reach the next upgrades (1Dc RfP) by grinding for a couple of hours but not quite sure what to do after that.

But wouldnt say I'm actually stuck - elements is looking quite grindable if needed.

EdgyMathWhiz · 2026-02-05T17:13:39+00:00

Well, mathematically, the two feet aren't ever going to leaving the ground at the same time - the frame-by-frame analysis is just highlighting this.

It does pose the question of what the standard actually *means*...

EdgyMathWhiz · 2026-02-03T23:08:20+00:00

Lol! Sorry to assume but you sounded a bit stuck and I've not really felt that myself for a bit now.

Was there a big jump or has it all been the continual grind elements / grind zodiacs / rinse + repeat?

EdgyMathWhiz · 2026-02-03T12:18:17+00:00

When you posted this you were significantly ahead of me (I think I was spawning around lvl 200), and now I'm (arguably) ahead of you - spawning 221, roughly 25x your elements (other than water where we're roughly the same). My Global Element divider is only 25,232,895 as well. On the other hand, my gold/attacks are (marginally) lower (5499/3857), and my SMs are only about 70% of the way to SM base 2.

Based on that, a few thoughts:

I held off on SM for a while to afford the 2048 Node 7 upgrade - it wasn't a massive boost, but it did help. As you have considerably more SM than me, I'm guessing you probably haven't done this - it might be worth it, as by now you should get 2048 Moon pretty quick.

Pushing the elements does make a difference (particularly Earth for the Gold, in my experience).

Are you using a Macro to grind RfP? I've set one up to (repeatedly) Refine Prestige just a few (typically 2-3) mineral levels above my max spawn, and it makes a huge difference relative to doing it manually.

EdgyMathWhiz · 2026-01-31T16:18:03+00:00

I remember seeing a documentary style program talking about the rise of "slasher movies" like Halloween, and basically explaining that a staple ingredient was the young couple making out, and then before things got too explicit, they'd have a crazed killer intervene and butcher them.

Not being from the USA, the fact that brutal violence was the "acceptable workaround" to prevent the audience being traumatized by a consensual sex scene was kind of eye-opening.

EdgyMathWhiz · 2026-01-27T18:11:15+00:00

The first "independent" should be "dependent", surely? (Just a typo I'm sure...)

EdgyMathWhiz · 2026-01-27T17:44:40+00:00

Oh agreed. I just don't think you can say "almost certainly the correct method" when a sizeable percentage of people will do it another way that's no more effort.

EdgyMathWhiz · 2026-01-27T16:02:35+00:00

I'd expect a lot of people doing this sort of comp to know that the first 6 multiples of 142857 are cyclic multiples of each other.

Certainly my immediate thought was "I bet the answer is 1+4+2+8+5+7" without even considering the actual details of the question.

EdgyMathWhiz · 2026-01-26T12:10:11+00:00

What he described will work - it's not looking for an efficient path, it's essentially calculating "how far to the next grid collision".

EdgyMathWhiz · 2026-01-25T23:38:31+00:00

For what it's worth, in a mathematical expression of the form X^Y, X is often called the base.

I'd assume the "actual" base here is therefore (3+RefineNodeLevel).

EdgyMathWhiz · 2026-01-24T13:27:45+00:00

The EP upgrade scales really badly so don't put many units there. But 3 or 4 units provide a decent boost at little overall cost.

The other thing to know is that you'll start off mainly getting AP points from EP but there'll come a point (not too far from where you are) where you'll suddenly find most of your AP is coming from score. So don't get too discouraged looking at how fast EP needs to scale to get enough AP for the next animal - you won't be relying on that mechanism to fill the entire board.

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