pjs36

That's a fair point, that it's the most reasonable default. So I guess I'm just surprised I couldn't get it to work with an equals sign. COUNTIF(E609:J609,=P1) throws a syntax error

I shall, once I can -- in 6 minutes! I still am amused that equality checking doesn't require an equals sign in this case

In either case you were helpful, thank you @Burgi

And what you suggested worked! I was just formally asking it, like Journeyman suggested. You can answer, or not; I'm sure someone will, or I'll be downvoted into oblivion :)

I guess that is for @Burgi, by JG's suggestion

I even tried to search before posting, in case there was a fairly-immediate duplicate (I never know the terminology to use, most of the time)

Alright, it has been posted; here is to hoping I Haven't committed any major faux pas

OK, I can certainly ask a question. I really have no idea what SU is for; I'd assumed it was for Unix questions, but tried to google about SE and excel

What a handy world we live in. I'll check that out, but I expect you're right :)

Ah, I've only seen IF(E16:J16,"=CONST") type constructions. Can I really replace "=CONST" with a cell reference, and it checks for equality?

(Really I should say I'm trying to display rows in which one cell contains a given number, not count them)

This is the exact situation. I'm counting matches with =IF(COUNTIF(E16:J16,"=29")>0, "yes", "") to see how many cells have 29 as their data. But I need to check various numbers, and don't want to re-drag my formula as I check each one. I'd rather check if they =P1, say, where I store 29 in P1

Let's suppose I'm using Excel (really Google Sheets) and want to compare if two cells have the same value. It's easy to ask how many times 42 shows up in a column, but I can't figure out how to ask how many times (the value of cell) A1 shows up in a column. What am I missing?

There is a nice little phone game (Wyvern) I play sporadically, in which this is exactly the case -- if a spellcaster wore anything heartier than run-of-the-mill cloth (or maybe it was leather), they had a significant chance of "bungling" the spell.

And I'm interested to see where it goes! If you do find something nice, I'd love to hear about it. Or if another computer search would help, I'd happily lend a hand (I'm curious if there are multiple types that "decompose" into cycles. I suspect there are, but I really have no idea)

@arctictern Summer session just started, so it'll take me a few days, but I'll get something up there, hopefully sooner rather than later

Have you continued / do you plan to continue thinking about the problem from the algebraic side of the fence?

I was thinking about posting an answer to the question at some point, basically saying that it turns out to be a (fairly) well-studied problem in disguise, and linking to the relevant OEIS pages. In addition, I'd post the numerical things I found for n = 4 (orbit and stabilizer sizes), as well as a picture of a representative colored total from each orbit.

There are some with symmetries-of-the-square dihedral symmetry, though.

And I think I realized why none of the totals have full dihedral symmetry. Any permutation in Sym(8) that stabilizes a total necessarily permutes the seven synthemes. But $S_7$ has no elements of order 8. (I only realized this after seeing checking each of the 6240 totals, to see if any were stabilized by an 8-cycle...)

And just for fun, a colored total i.sstatic.net/sDexQ.png

(Sorry for bombarding the chat, but I thought it might be of relative interest, and didn't really have a better way)

And of course, the number of orbits was referenced in the OEIS page on the number of totals...

For n = 4, it would seem the orbit sizes are 2520, 1680, 960, 630, 420, 30, with corresponding stabilizer sizes of 16, 24, 42, 64, 96, 1344. I have representatives from each orbit too. Thankfully I printed them out as the computation ran, because it would seem my method of saving things is acting funny...

Alas, it was amateur programming, yet again: I was doing something for each total in a set of remaining totals (those whose orbit had not yet been found), while making the set of remaining totals smaller with each iteration. It would seem the set of remaining totals in the initial for loop was held constant, so that even totals whose orbit had been found, were being investigated again. An easy fix, once I suspected it was the problem!

Did you end up finding anything about orbits? Still fighting the computer over here, to an almost comical degree...

Yeah, I felt like I should have known enough about it to know that it was the same problem you were asking about, but I wasn't really familiar with it.

So I should have found the orbits ten times over by now, but GAP keeps crashing (and Sage does almost all of its group theory stuff by borrowing GAP stuff, from what I can tell). More accurately, I apparently overstay my welcome. I get error messages like "the session in which this object was defined is no longer running." I'm sure I'll be able to find a way around it, but it's crashed in the middle of the 3rd orbit several times now...

@LegionMammal978 I think the question is fine here, it's a chatroom for crying out loud. According to Wikipedia it's dimensionless. So maybe it's analogous to writing $1 \text{doz} = 12$.

(So if you're familiar with graphing functions using transformations, it's about how $y = x^n$ looks very different at $x = 0$, depending on whether the exponent is even or odd)

I think "the component of A in the direction of B" is more often called "the projection of A onto B" ?

I guess I meant $r = 10$, not $2$.

I think you probably have a block design, and there are a couple of formulas relating $v, b, r, k, \lambda$ (so many parameters!). I think for you $v = 12, b = 20, r = 2, k = 6, \lambda = ??$ (may not be possible)

Yes, I know what you mean. Figuring out "what everyone else is calling the thing you're looking at" is often a nontrivial task -- it just happened to me, with something I've been looking at the last few days.

Of course, it may well turn out that it's just easier to figure it out yourself, than get sucked into terminology and literature etc. :)

Unfortunately I found the terminology curve to be pretty steep for design theory, but it's worth a shot to look at this list and see if you can identify what "kind" of design you're after. Then, you can try and figure out what its parameters are, and there are huge databases of designs out there, that probably have what you need.

@MichaelP. I suspect what you're doing falls broadly under the heading of "combinatorial designs". I'm not an expert, but any time you have lots of sets and symmetry (they all contain this many, overall any element is included this many times, they all have this size overlap, etc), that's what comes to mind.

Yeah, that's the one

I guess I am worse than ever, because I seem to end up integrating $\sec \theta$ (times a constant, maybe)

I don't see why trig substitution would be so bad, or am I worse at calculus than ever before?

Here's another picture if anyone is easily amused by colors and graphs.

They'll say, "Aw, sweetie, at least you're trying"

Well, that's true -- it does have a "certain look" about it :)

I take it you also clicked on the picture, @s.harp ? There's a bit more of an explanation in the image description.