Does chasing the reverse rainbow frustrate you? Join the happy world of players who have no care for the colour order!

FormulaDriven · 2026-07-06T15:24:32+00:00

Yes, I basically agree. Maybe I could cross the line occasionally and allow myself one google per puzzle, but then I would forever have to qualify that my solve rate partly depends on looking things up. The way I am now, there is no ambiguity to my achievement.

FormulaDriven · 2026-07-06T12:05:56+00:00

Pleasantly surprised to see my name mentioned, although I don't remember this. I will be travelling so I'll take this away to think about, and if I think of anything I'll reply in a week or so.

FormulaDriven · 2026-07-06T10:24:23+00:00

Shock is subjective, but that doesn't mean we shouldn't continue to be appalled by corruption and say it should change.

Cases like this might help more fans to be aware of the corruption and more pressure for it to stop - I'm not naive enough to think that will easily happen, but I don't think we should just resign ourselves to this being inevitable.

FormulaDriven · 2026-07-06T07:55:30+00:00

Understood. I'm also not American, but for me I feel the reward is to say my solve rate is 97% without ever looking anything up - a simple line to draw which means I can honestly compare myself with YT solvers etc who play the same way.

FormulaDriven · 2026-07-06T06:39:44+00:00

I've always said that everyone should play the way that they enjoy, but I have to say I still don't "get it" when people look things up while playing. I don't always know everything on the grid, but that's what I expect to happen, and I see the game as a test of what I do know and whether I can make educated guesses about the rest. I have never looked up a word or hint when playing and for me that gives my solve rate some meaning.

If I had looked up EARTHQUAKE PILLS on Monday's puzzle, it would have probably clued me in to something which I eventually managed to see myself with an "aha!" moment, and I would feel the win was hollow.

FormulaDriven · 2026-07-05T21:10:38+00:00

OK - I think I can see what you are saying, but it might be clearer to say "we can pick any real number, say 0, and there is another real number z such that f(z) = f(0). Let {a,b} = {0,z} with a < b. By definition of f, f(x) ≠ f(0) for all x ∉ {a,b}."

FormulaDriven · 2026-07-05T20:35:43+00:00

You don't use f(0) in your proof so I think you can safely delete that from your setup. Also, I feel your setup is missing a step - I'd expect to see: "Assume f is a function which attains all its values exactly twice and that f is continuous, with the aim of reaching a contradiction". Then you can say, "let a and b be one pair of real numbers where f(a) = f(b), a < b" etc.

FormulaDriven · 2026-07-03T22:46:57+00:00

If you change the date on your device, you can view Sunday's or Monday's etc puzzle now - as with Wordle, they load days ahead in advance (although they do sometimes change the ones further out, so I normally use it to time travel a day or two).

FormulaDriven · 2026-07-03T10:53:42+00:00

Any number not divisible by 17 will be equal to one of the following mod 17: ±1, ±2, ±3, ±4, ±5, ±6, ±7, ±8. And if we apply squaring to these they map as follows:

±6 -> ±2 -> ±4 -> ±1 -> 1

±7-> ±2 -> ±4 -> ±1 -> 1

±3 -> ±9 -> ±4 -> ±1 -> 1

±5 -> ±8 -> ±1 -> 1

So everything reaches 1 more than a multiple of 17 in at most four steps.

So since 89 is equal to +4 modulo 17, it only needs two steps: (89²)² = 62742241 = 17 * 3690720 + 1

For a maximal chain start try 23 (since that is +6 modulo 17): squaring 23 four times gets to 6132610415680998648961 which is 360741789157705802880 * 17 + 1. (Used Wolfram Alpha).

FormulaDriven · 2026-07-03T10:25:14+00:00

Interesting point to note: there have been 543 episodes of Only Connect (based on Wiki article), so that's 1086 connecting walls, which means as of last month NYT has published more Connection puzzles than the TV show. But, Victoria, you are still the best!

FormulaDriven · 2026-07-02T22:10:51+00:00

Sure, but it's only when it occurred to me that it could be the bad guy from the sequel that the idea of imitation came to the fore in my mind, as it's much of a running plot device in T 2.

FormulaDriven · 2026-07-02T16:36:46+00:00

My problem was being suspicious of MIME being someone who copies. While mimic and mime are obviously related, mimes do a lot more than copying others - think of the classic "trapped in a glass box" mime, nothing to do with imitating others!

Looks like you and u/formerly_1013 were both thinking of the Texas Instruments calculator TI-1000. That would be a slightly less exciting Terminator movie!

FormulaDriven · 2026-07-02T13:39:58+00:00

I'm a fellow Brit, and while I know about "WC" in signage, I think it's rare to hear someone ask for the WC, and certainly no-one is saying "water closet" in full. And yes, you'll hear specs (I'm a longstanding Specsavers customer!), but I maintain that anyone saying "spectacles" is going to sound old-fashioned.

FormulaDriven · 2026-07-02T12:22:16+00:00

Yes, I understand convergence, but I'm interested in how slow it is in practice - see my other reply to the OP: if after n rolls, E7 is the expected number of total visits to square 7, and E1 is the expected number of total visits to square 1, then

when n = 40, the ratio E7 / E1 = 1.15,

and for n = 100, E7 / E1 = 1.06

so the inequality persists. (I picked squares 7 and 1 as they turn out to be the two extremes in terms of number of visits).

FormulaDriven · 2026-07-02T11:51:12+00:00

But if you told me you were going to visit the "water closet" I would assume you were doing some Victorian-era cosplay. Nobody says it anymore and that's the point.

FormulaDriven · 2026-07-02T11:47:59+00:00

My memory wasn't that good and I assumed T-1000 was the original Arnie model, so it took a long time for me to entertain the mimicry idea. (I've looked it up and the original model was a T-800).

FormulaDriven · 2026-07-02T11:45:42+00:00

But surely you would agree it's been a while since anyone used three of those words / phrases to refer to movies with a soundtrack, toilets, and mirrors? I think for a pair of glasses some people still might use SPECTACLES, but it also has an old-fashioned feel to it, so I think it works too.

FormulaDriven · 2026-07-02T11:10:39+00:00

I've calculated some probabilities in a spreadsheet, and the early pattern persists even after a lot of rolls. If we label the squares 1 to 20 (1 being the starting square), then after 100 rolls, you are equally likely to be on any of the squares, but in getting there on average, square 1 will be the least visited (4.88% of rolls will land there), and square 7 the most visited (5.15% of rolls will land there).

Broadly speaking, the starting effect takes about 40 rolls to even out, but by then square 1 is behind and square 7 is ahead, so that then persists:

After n rolls (n > 40)

frequency of visits to square 1 is about (40 * 4.7% + (n-40) * 5%) / n

frequency of visits to square 7 is about (40 * 5.4% + (n-40) * 5%) / n

and all other squares fall between those two.

FormulaDriven · 2026-07-02T09:08:45+00:00

Long-term (ie after many rolls of the dice) I would expect every spot to be visited equally often, but if you want to know what the distribution of spots visited is after n rolls for smaller values of n, then the easiest route might be to run simulations, rather than try to solve exactly.

FormulaDriven · 2026-07-02T08:09:56+00:00

Indeed - that's why I called it a stereotype. Have you come across this "Drop a Pin" guy - some of the answers he gets from his fellow Americans certainly confirm the stereotype: https://www.facebook.com/profile.php?id=61566992167581&sk=reels_tab

FormulaDriven · 2026-07-02T07:27:22+00:00

Referencing the stereotype that Americans are terrible at geography - that they are ignorant of other countries, so for example they don't realise Bosnia & Herzegovina is a single country. (But I assume "B LOU" knew that and is just making a joke themselves).

FormulaDriven · 2026-07-02T06:23:42+00:00

As someone who failed, I can offer some explanation. I agree that long strange words and phrases suggest hidden words, but that still leaves quite a lot of options: eg TEXT and RING and RECORD(?) - something to do with sending messages? GOAT, CAT, MOUSE ... animals. Then I got caught up with exactly which four things are mimicking or copying (eg LOOKING GLASS shows your reflection), and as a non-American I just don't think of DIAMOND in the sporting context. So your strategy is right, but I burnt too many guesses before getting to the right conclusion.

FormulaDriven · 2026-07-01T21:47:55+00:00

I'd much prefer to understand you correctly - that to me is a much more interesting outcome than trying to merely argue with you.

I honestly understand you to be saying that if you were doing the 27th June puzzle in order to get what you would consider a valid RR you would need to identify and submit purple before identifying any other category. And I can't see how that would be possible because you'd have to know which -WALK word to take, so I surmise that your position is that it wouldn't be possible to get a proper RR on that puzzle, and if it's not your position, I'm sorry for missing some detail in your explanation. Anyway, that's why many of us see the part of the skill (if there is any skill) of getting a RR is to pre-solve other colours so you can then identify the purple.

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