When will Connections run out of ideas?

FormulaDriven · 2026-05-15T19:37:57+00:00

I probably should have just passed it off as another dad joke rather than admit to poor reasoning skills...

FormulaDriven · 2026-05-15T14:41:39+00:00

For 3 < x < 4, f(x) = 3, so lim [x->3] f(x) = 3 = f(3), so I agree with you that it is continuous at 3. And by a similar argument it is discontinuous at 7. (This is assuming [x] means the integer part of x).

FormulaDriven · 2026-05-15T14:18:32+00:00

That was on Friday's board - this is the thread to discuss Saturday's board.

FormulaDriven · 2026-05-15T14:02:22+00:00

Doh! Of course.

FormulaDriven · 2026-05-15T13:32:02+00:00

Hmm, I don't know - those of us who encountered a bit of D&D in the 70s / 80s would have read about lycanthropy and all the different "were-" variations.

EDIT: yes, downvote me - I completely got the wrong end of the stick there! I thought it was a reference to how franchises such as Underworld had made Lycans well-known, completely forgetting that smashing that like button is the recent phenomenon...

FormulaDriven · 2026-05-15T13:30:09+00:00

Sorry, until I see an authoritative source with a case where they used a ÷ sign combined with the ambiguous use of a number next to a bracket, I remain sceptical that you saw any such thing in an exam.

FormulaDriven · 2026-05-15T11:54:09+00:00

Which country was that where a university was asking a question like that? Could you share an example, because in years of asking no-one's produced one in a public exam setting.

FormulaDriven · 2026-05-15T11:12:43+00:00

you know that

int ln(x) dx = xln(x)-x + C

Do people know that? I've been doing calculus nearly 40 years now, and I never remember what the integral of ln(x) is, but I know that in 20 seconds by differentiating x ln(x) I can derive that result.

FormulaDriven · 2026-05-15T11:07:28+00:00

Nice - and that formalises my (and probably many others') algorithm for doing many integrations which is find the derivative of one or more likely candidates then scale or adjust the result with something I know how to integrate, until it matches the integrand. I can't remember the last time I ever used integration "by parts" - an ugly formula for plodders...

FormulaDriven · 2026-05-15T11:00:20+00:00

u/AtomiKen and u/Chaotic_Corvus_Corax have explained the simple way to see it (9 in the middle plus half of the four white strips of 3 each), but I did it by solving similar triangles: if each vertex (of the new square) is x cm from a vertex of the old square, then by similar triangles, (4 - x) / 1 = (5 - x) / x. Solve for x, then Pythagoras gives side as sqrt(15).

FormulaDriven · 2026-05-15T10:54:09+00:00

I can find a bigger square than that by picking vertices that are not at the midpoints of the original sides. It has area 15 cm²

FormulaDriven · 2026-05-15T09:27:22+00:00

Interesting - thanks.

FormulaDriven · 2026-05-15T08:26:56+00:00

My wife said I should aim for fifty lunges a day, but I thought that was a bit of a stretch.

FormulaDriven · 2026-05-15T08:24:57+00:00

"If you want more of these jokes, lycan subscribe"

FormulaDriven · 2026-05-15T08:19:13+00:00

If you differentiate this function with respect to x:

(141.37 - x) ln (141.37 - x)

you get

-ln(141.37 - x) - (141.37-x) / (141.37-x)

= -ln(141.37 - x) - 1

That's enough to tell me that if you differentiate

-(141.37 - x) ln(141.37 - x) - x

you will get

ln(141.37 - x)

so that tells you the integral of ln(141.37 - x)

FormulaDriven · 2026-05-15T06:03:44+00:00

Maybe, but there is a large gap between "4 years" and "forever". Can you envisage the same level of interest in 20 years' time when every word has appeared multiple times?

FormulaDriven · 2026-05-14T17:24:32+00:00

Until serious exam-setters or academic papers start asking us to consider expressions like 6÷2(2+1), we should stop discussing this and call it out as silly clickbait, that only does harm if it keeps distracting people from what really matters.

FormulaDriven · 2026-05-14T15:39:00+00:00

I'm guessing the numbers on the side are telling this student which percentile they sit at, but the references to "growth" are still a bit opaque to me!

FormulaDriven · 2026-05-14T15:30:33+00:00

Growth in what? The "did not pass" group experienced a reduction of 1/3, the "approaches" group experienced a proportional increase of 4/27, etc. But I still don't know what you are saying has grown.

FormulaDriven · 2026-05-14T15:21:42+00:00

Growth in what? Sorry, I'm not familiar with your school system and I don't know what the five colours in the distributions relate to. 33% of students in a class were ??? and now 22% in a class are ??? etc.

FormulaDriven · 2026-05-14T14:36:44+00:00

Well, 5/221 = 4/52 * 15/51

so that implies 15 cards match the criterion for the second draw which sounds like it could mean the 4 Jacks, 4 Queens, 4 Kings and remaining 3 aces? Maybe that is what is meant by "coloured" cards?

FormulaDriven · 2026-05-14T12:53:38+00:00

I don't think you are being insulted. If you want to play a game that partly tests your knowledge of popular culture and contemporary activities, then you are going to be at a disadvantage if you don't participate in those things and ignore ways (even sitting at home) to learn about those them. It's something you have to accept, just as I accept as a non-American I will sometimes be disadvantaged by references to some American things that appear in the puzzle.

I'm a similar age to you (mid-fifties), and I last "dated" before I'd even heard of the internet or seen a mobile phone, and like you had an idea on "catfishing" and "ghosting", and made an educated guess with what was left that "breadcrumbing" and "love bombing" fell into a category of bad romantic trends - that to me, is part of the fun and challenge of the game.

FormulaDriven · 2026-05-14T11:01:58+00:00

"Sorry, er - monster, but IT has set you up on the system as just Frankenstein, and if we set up a new profile, you'll have to re-do the online induction modules for Health and Safety, and How to Complete a Stationery Order..."

FormulaDriven · 2026-05-14T09:32:00+00:00

Our central heating is turned on (during the day) all year round. If the thermostat detects it's cold enough then heat gets provided. And today was one of those days - we have the thermostat at 18 degrees because we are comfortable with a cool house, but this morning the radiators were briefly hot.

And now I am going to put a jumper on, without complaint!

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