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Sunday, 9 July 2017

Thoughts After Protospiel.

So, over the course of this weekend, I was at an event called LFG Sydney - basically a boardgame convention, that runs once a year. And as part of that convention, they hold a workshop called Protospiel. It's for board game designers, where they can bring along their prototype, show it to other designers, playtest together, and also do a quick pitch to publishers, get some feedback, etc.

There were about twelve of us there who were designers, plus a few extra playtesters. I think mine was one of the freshest - I'd been working on my game since about the end of March, whereas some of them had been going for years. Though one did have a game that they'd done in the last six weeks! And their art was incredible. (They did it themselves. Advantages of being a graphic designer/artist as well, I guess!)

Firstly, it was a lot of fun. I got to meet a bunch of other game designers, who were mostly a little older than me, see a bunch of cool games, play a few of them, and get my game playtested. It was the first real playtest - I had done a quicker one with my brother earlier in the week, but that was really just trudging through it to see what worked. I also met someone else later in the day who, after playing their own prototype, was interested in having a go at mine. It was then that it was confirmed for me that Septimus is absolutely terrible as a two-player game. For the earlier playtest, there had been four players, and it had been quite fun; this wasn't fun. For the first little while, it was okay. But then, it got tiring. Hard. A bit after we got into the middle, we both called it quits.

But this is good to know! And that doesn't surprise me too much. Often in two-player games, you'd choose heroes that were on opposite sides of the board - so you're not going to go anywhere near each other (unless you're trying to) until you're right in the middle. And even then, only really if you want to. Even three players could mostly be by themselves. When we had four, they started interacting fairly well, but they still wanted that a lot more. I think the optimum number for the game would be five. I also think it could get cramped with seven, but I'm not sure.

But I got a lot of good feedback from that playtest at Protospiel. Even though there were some things that didn't work too well, they still generally enjoyed the game, and each of them could certainly see potential in it. Which is encouraging, considering how young it is! However, it really felt too much like a solo game a lot of the time. You were just doing your own little thing, and the little bits of interaction weren't really meaningful enough. And the choices you made didn't seem to matter, a lot of the time. And all the numbers in the game really worked against the story aspect of it.

And on reflecting a bit after this, I realised that what they were saying actually made rather a lot of sense. I had built the game around a particular story that I had constructed in this fictional world, where seven Heroes are sent into a Maze, each starting at different corners, all trying to get to the centre. And, in that story, they wouldn't really interact much. That's not the point. I mean, they are trying to get to the centre first. But they can't see how anyone else is doing - it's the Middle Ages, there aren't trackers or anything! It's just them and the Maze. Which isn't really that great if you're trying to do a multiplayer game, strangely enough! But could be really interesting for a single-player experience.

But then, I've also got this world that I've already put a lot of effort into building, and these seven factions, the Septem Septimus, and the different flavours, playstyles, etc., that they have. (It's really rather similar to the MTG Colour Pie, for those who play Magic.) And that was certainly one of the points that different people all really liked, and thought was interesting. So that's a world that I can create other experiences in, other games in. Maybe a seven-player co-operative game. Maybe a simpler, smaller game for a few people. Maybe quite a few different games! I don't really know yet. But there are a lot of possibilities that arise from that.

So yeah. Don't have any plans just now. I've been intensely working on that over the last week - well, and further back than that, to get it ready in time - so I'm going to take a break from it for a bit, more than likely. But I'll come back to it before too long, and then we'll see what we come up with :)

Thursday, 6 July 2017

Building Games With Story.

As I've written about before once or twice, I'm working on a board game called Septimus. I've now actually done all of the printing, and have all the parts - though I could probably use some more dice. I can get dice easily enough, though. That's not too hard.

I just spent way too long looking up 100 packs of d6s. *sighs* Actually can't seem to find an easy way to get them in bulk, at least not in different colours. I'll keep hunting around, though.

Anyway. That's not what I wanted to talk about. What I wanted to talk about was the difficulty of building games with the story at the centre, which is what I'm trying to do with Septimus. And also, solving multiple problems with one solution.

What I mean is this. A lot of games have some sort of story to them. But most of the time, it's somewhat tenuously linked to how it works mechanically. Choices are always made in favour of making the game work, rather than making the story work. Because the game is more important!

And it is, in a sense. But with this game, I wanted to develop it in such a way that all of the mechanics, as much as possible, made sense from the perspective of story. They should also have a purpose mechanically, of course. But they should make sense within the world that I'm building.

I'll give you the example that I've just been struggling with. So this whole game happens within a giant underground maze/dungeon type thing. With lots of rooms that you go through, and each room has an encounter that you have to face, to both get closer to the middle of the maze, but also to get skill boosts and items. Now, this is all set within the Middle Ages - at about the time when black powder was happening, because that's what one septimus (clan/faction) is focussed around (they were pretty much going to be the wall removers, but then I've taken out walls from the game, because they weren't working; so they're now much more along the actual flavour of Red in MTG). There's no magic. And so the idea was, that when an encounter is revealed, it stays there for the rest of the game. Which makes sense, story-wise. Rooms don't really shift around and move too much, particularly not without magic, or some serious modern-day tech, and especially not underground.

And I created these Encounter Markers to help that - to show which space on the board an Encounter was tied to. They're rather fidgety to sort through, but they're helpful.

The thing is, though, the way that the game plays out, even if you have less players, you're revealing most of the encounters on the board. There are seventy spaces. So probably around sixty cards, let's say, each 8.89cm x 8.89cm. That adds up really quickly, and your playing area grows and grows. If you're playing on a table, that doesn't really work too well. If you're playing on the floor, it doesn't matter so much, but it's still awkward. But I can't really make the cards any smaller - I need that room for all the rules text, the numbers, title, and it's nice to have some flavour text and art as well. (I don't have art at the moment - just a space for it.)

But I realised that this was a problem, and going to be more of a problem the more players you had. It's supposed to work with up to seven players, being optimal at probably four or five. So yeah, there wasn't going to be enough room.

As such, I introduced a new mechanic. The shuffle.

"At any time during a turn — except when an Encounter is being drawn or faced — any player may declare a Shuffle. When this is done, all visible Encounters are shuffled back into their respective decks, and the Encounter Markers put back, except for ones that Heroes are standing on. All other spaces now revert to being Unknown, and are drawn again as normal. If you draw an Encounter that you have already defeated, follow the rules further down. A Shuffle may occur a maximum of once per round; also, the same player may not declare a Shuffle twice in a row."

Unknown spaces, fairly obviously, are spaces where you don't know what's there. If you draw an Encounter that you've defeated, you get a free movement to another space, or can just end your turn if you so choose. A round is when all players have had one turn. I decided to leave in the Encounters that players are on at the time - because that makes sense from a story perspective. All these rooms are shifting and changing around you, but your room doesn't change. It might move to a new location, or something - but that would be complicated to do. I also could have done it that rather than being shuffled back into the deck, they were just shuffled into themselves, and then immediately drawn again until they are redistributed around the board. But that both takes up too much time, and completely misses the point of what I'm trying to achieve with this mechanic.

The idea is that with this, you will have less cards out at any one time. If the encounters that are out at the moment seem too difficult for you, you could declare a shuffle, hoping to get some easier ones. If you think that someone else is just having a super-easy run of it, you could declare a shuffle, hoping to make it trickier for them. But it's going to affect everyone, of course.

Now, there are a couple of things that don't really make sense here, story-wise. I've already mentioned that in that time, rooms really aren't going to be able to move. But hey - the Ennius are master builders, love mechanical things, and I've already got lots of other rooms that I can't explain from a Middle Ages standpoint - particularly not in just a 10m by 10m space or so! So I'm sliding over that a little, so that it will work better as you play.

It also doesn't make sense that one Hero would be able to know what's happening with another one. They can't really have tracking devices or anything, monitoring cameras. A map with little coloured dots showing the other Heroes. Now, again, I might be able to come up with a way for each player to mark their route in secret, perhaps only revealing it when they go to a Junction Space, or something similar. But that's really, really annoying to make work for multiple people at the same time. One person, that's okay. Multiple people? Yeah, no. So I accept that as something that I really can't do anything about.

I mentioned at the beginning that I would be solving two problems with one solution. What were the two? Well, the first, as I mentioned, was the game taking up too much space. The second is that, on opponent's turns, players don't have much to do. I mean, you can watch, and hopefully it's an interesting enough game that that's enough. And some of the players do have Abilities that they can use on an opponent's turn; and there are some Items that work that way too; but not all do. So this gives players another opportunity to be able to do something on an opponent's turn.

Hope you've enjoyed that little look at mechanics, story, and board game design!

Monday, 12 June 2017

An Infernal Line of Reasoning.

A note before I launch into this: what I'm talking about is a super-controversial issue. I expect that many, if not most, people will read this and disagree with most or all of what I'm saying. But I'd appreciate it if you could not just shout hate, and rather give a reason for what you think or feel. That would be great.


So the other week, I finished listening to the audiobook of Inferno, by Dan Brown. (Yes, it references Dante's Inferno quite a bit.) It's the one that relatively recently got turned into a movie. Don't watch the movie. People have various attitudes towards Dan Brown books, but I'm a bit of a history buff, so I love the detail. I also loved how in this book, there were more turnarounds than you could poke a stick at. Classic drama. (One of the reasons that the movie fell through was that they really only included two of them, whereas the book had easily half a dozen or more.) Also, by the end, you were able to empathise with the supposed 'villain/s'. Which I rather appreciate. There's a bit too much hate that goes around.

Here is where I'm going to be doing a massive spoiler for the book, so if you don't want that, stop reading and go watch something else. Or read the book and come back. Not the movie, they changed the ending for it. Yes, they actually changed the ending. That's how bad it was.

Okay. If you're still reading, I'm assuming that you're okay with massive spoilers for the book.

Throughout the book, there are big hints at disease and epidemics. References to the Black Death. Biohazard symbols. The World Health Organisation. Plague masks. The whole idea is that Langdon and his partner are racing to stop someone from releasing a plague that will go global, and wipe out some percentage of the population - the idea being that the humans left surviving will then be able to thrive, because there will be less competition for resources. The analogy is used of the Black Death preceding the Renaissance. So the whole time during the book, you're given these grisly images of disease, death, horrible pain and global panic.

But right at the end, this virus (because it is a virus) is actually revealed to be something very different. It's a sterility virus. Mass Effect players, think genophage, but not quite as bad. Essentially, 1 in 3 people, for the rest of time (unless a cure is devised) are rendered completely infertile. Works on both males and females, and it's suggested that because of the brilliance of the person that engineered the virus - and the fact that they committed suicide - it is going to be extremely difficult, maybe impossible, to come up with a cure in any near future. As an aside, they don't manage to stop the virus from getting out, basically because they got their dates wrong - so it's gone global.

A couple of people in the book have a very immediate and visceral reaction to this virus. They hate the idea of it, think it's horrible, and do anything that they can to stop it. But others - they see it as a clean answer to many of the problems that we face in the world. Overcrowding. Pollution. Resource depletion. Food scarcity. Poor health in some areas. The simple fact is - if you have a lot less people living on the planet, suddenly, many of these problems become much more manageable.

Strangely enough, I finished that book thinking - well, actually, that would be a great idea. Overcrowding has been in the back of my mind ever since I read a comic of Mandrake the Magician, where he met someone who had time-travelled back from a future where they had serious overcrowding; to the point where they had people who's job it was to cull the population. Now, I don't know if we'd ever quite get to that stage. But certainly, in many places, you have a lot more kids being born than people are able to take care of; because of lack of contraception, or lack of education, or lack of wealth or health, or any number of other reasons. And there are so many kids that are orphans, or waiting for foster carers, or that are just left, because people can't care for them. And I don't think that's really okay.

Now, don't hear me saying that we shouldn't have kids. Or that everyone should just stop having sex! Like that would work. I'd be the last person to say that. I've been aching to have kids for a long time. But, although I know I'd enjoy having my own child - I also think I'd really love adopting children, and being able to provide them with parents. I think that would be super-special too. And yes, it would be hard. And sad. I know there are a lot of people that would find it particularly difficult - guys that see themselves as having their masculinity robbed from them, or girls being broken over not being a mum to their own kids. Though perhaps some would be glad to not go through all those pains of giving birth....but I'm straying well into the territory of things I know nothing about.

I don't really know. I think it's an interesting topic to think on. Because our population is skyrocketing, any old graph can tell you that. Growing at an exponential rate. And as it grows, so do so many other issues. And most things on this Earth are finite. Some are a bigger finite - but almost all will run out, one day. And if we don't look to solving that issue soon, it's going to come back and bite us on the bum before we know it. That's my thoughts, anyway. You can feel free to disagree.

Difficult Virtues

I turn 25 later this year.
Which makes younger me rather sad.
Because younger me thought that by now,
I would be married,
and have kids.
That I'd be a dad.
And I'll admit,
that every time I get to play with younger kids,
it's both a great joy and sadness.

A great joy,
because I'm doing
what I wanted to be doing.
A great sadness,
because it's only for a moment.
These aren't my kids.

And sure.
I don't have to deal with the crazy hours.
The various bodily fluids.
The noise.
The tempers and complaining.

I'd take it all in a heartbeat.
Just to be a dad.
But it's not the sort of thing that you can short-cut.
Well.
You can.
But I'd rather not.
*sighs*

Patience.
It's a virtue.
That is difficult.
Sorry younger me.
There's rather a ways to go yet.

Saturday, 10 June 2017

Some Recent Notes.

Thought it was time for another post. I have a specific one I want to do, looking at a book I read recently, but I think that will be for later.

I still haven't talked about SWF, so I'll do a section on that here. Then there's a few other things happening that I thought I'd chat about.
The Sydney Writer's Festival was quite a bit of fun this year. I got to do a lot of the school days and children's events, which I hadn't before, so loved that :) Went around a bit, as well - was at the wharf (Walsh Bay), of course, but then also at Campbelltown, and out at Penrith, and had an early day helping at the office, which was cool. Had one day that I was helping an older lady, and got to sit in on her events - which was awesome, because they were both sold out before (so I wasn't really sitting, but you know) - and they were just really interesting. One was a panel on the attitude towards immigration in Australia; they talked a bit about how we're quite unique in that we're an island continent, so we can completely control who comes and goes by sea. Also had a bit of the flavour of the old 'White Australia' idea. Essentially, they - and pretty much everyone else in the room - felt that the government had a pretty terrible attitude towards immigrants and refugees/asylum seekers. Agreed. The second one was more historical - someone talking about their book on the Byzantine Empire, and particularly Constantinople; which I found quite interesting, because I'd just been reading Inferno (incidentally, the book I want to do a post on), that included a section on that. So that was cool. I rather enjoy history.

So. Recent bits and pieces.

I've become the worship leader for the PM service over at Cobbitty Anglican, which is significantly awesome. It's the sort of thing I've wanted to do for ages, so really enjoying that. It's also quite a smaller team, and a congregation size that's quite familiar for me, so a good place to start. Looking forward to seeing how that grows :)

I've been working on an idea for a board game, that I'm calling Septimus. I wrote about some of the backstory here, and you can see me talking a bit more about the design of it here. I'm getting pretty close to having the first draft done; over the last little while I've been getting it ready for printing, so that I can start playtesting. That's going to be fun :D But I've really enjoyed designing the different bits for the game, and figuring out how it's all going to work together.

I've also just gotten the final bits of video from my album launch back in September of last year, so I'm going to be working to get that released and out to people as soon as I can. Then I can think about getting the next album recorded....really looking forward to that one :) I might be biased. It is an album about love, after all.

I've been invited to be the speaker for another Cru Camp, happening in the first week of the holidays. It's a study skills camp for year 11s, and they've got a special keynote speaker coming in on the first day - Deng Adut. You might not know the name - but you'd probably remember his face from the new WSU ads. So if you know someone who's in year 11, definitely encourage them to go along! We're also looking for some teachers who can help tutor different subjects and such. You can see more details about the camp here.

While I don't have a job at the moment (apart from the one at the church, that is - but that's just a few hours a week), things are starting to look up. There are more possibilities opening up, more opportunities, more doors that are starting to open rather than be closed. And exciting ones! The hard part is always deciding which ones to take....

But yeah :) Though things have been tricky this year, I think we're heading towards a turnaround. And I can't wait :)

Sunday, 4 June 2017

An Argument For A Loving God.

I realise that I haven't gotten a post up for SWF yet. Hopefully that will be soon. But had this thought, so figured I'd write it out.

One of the big arguments that is given against the Christian idea of a loving God is the prevalence of suffering and pain in the world. If God was so loving - wouldn't he do something? Seems to be the basic idea, or something akin to it.

It's something that was tackled by John Dickson, in If I Were God, I'd End All The Pain. Definitely recommend you having a look at his argument at some point, because it's quite simple, yet I think quite strong. But I want to have a look at a different angle.

Let me ask you a question. Do you think that people are loving? On this earth - do you think that there are people that show love? Or even just one person - even just one person, that you would describe as loving? I think that most of us would say yes, we believe that either people in general, or some people at least, are loving, to some degree. A few more than others, perhaps. Mothers, or doctors, or firefighters, maybe.

Okay, then. Let's assume - for the sake of argument - that there is a God that has created everything. We take that as a given. And we take, as a given, that he has created us. We also take as given that he existed before anything else. (It's okay if you don't think that these are the case. Just using it for this point here for now.)

Now, a question. Can you create something - when you have never experienced it yourself? If you told a person to paint a tiger, if they had never seen or heard of one - how would they? If you told someone to make a sphere, but they didn't know what one was; could they do it? And similarly, if God did not know love, if he was not a loving God - how could he create loving people?

This, for me, doesn't make sense. How could an unloving God create people that are loving? How could an uncompassionate God create people who are compassionate? How could an apathetic God create people with empathy? I don't think it's possible. If we are all of these things - then God must demonstrate these at an even higher level than us. So, in a sense - the fact that we are asking why a loving God doesn't end all the pain, shows that God is loving. Because we are asking that question out of our own desire to help, out of our compassion and empathy and love.

It's quite possible that this isn't a watertight argument. I've just thought of the example of A.I. - if we can create A.I. that exceeds our own level of thinking, couldn't God do the same with human emotions? And perhaps it's possible. But I think there's a big difference between creating something that exceeds you at something you possess, that is better than you at something; than creating something that has something that you do not, that you are unaware of and have no knowledge of.

Please, feel free to discuss this - but nicely! :)

Tuesday, 30 May 2017

Every Day I'm Buskerin'

Okay, that's a terrible title. Oh well. Deal with it.

I'm a bit behind on my posts. Hopefully I'll have one up about the Sydney Writer's Festival before long, and another one about something else. But thought I'd do this one now.

On Saturday, I went and played on a keyboard in Camperdown Memorial Park in Newtown. Well. I brought the keyboard with me, and played on it. But you know. It was my first time busking with a keyboard, for various reasons. Power is a bit tricky. And you can't really take it on the train. But that wasn't the important thing, though it was pretty cool. Neither was it important that it was the first time I'd played a gig in about nine months or so, or that I hadn't played some of those songs in ages. Or at all in public. Though that was cool too.

No, the important thing was that it was for Busk For A Cure. To those of you who aren't aware, Busk For A Cure is an annual charity music festival that happens over at Newtown around this time each year. It's still in the early stages - last year was the first time it had some decent organisation happening, and so this year we had some good foundations to build on. I had heard of BFAC before, but hadn't gotten involved - but this year, they needed a few extra people on board, so I put my hand up :) Since then, I've been running the blog over here, and also working on a couple of press releases and such, as well as other bits and pieces. And it's been pretty awesome.

So that all came to a head this Saturday just past, when we got together in Newtown and made some noise! Well, music, hopefully. People seemed to like it (for the most part), which was good :) There were a few hiccups, as inevitably occurs with these sort of events. When you have fifty artists across five stages across the whole day, something is bound to go awry. But it all got sorted one way or another, and it seemed to go really well. We're still waiting on the final tally - that's happening tomorrow - but I'm feeling really positive :)

All the money raised goes towards both Cancer Council NSW and Crohn's & Colitis Australia, we don't keep anything for costs and the like. We have sponsors to cover all of that, as well as a great team of volunteers. It got started and is being run by Helmut because of his mother, who suffered from cancer. And it's pretty darn awesome. I'm super-stoked to have been involved with it this year, and am already looking forward to next year :)

If you are interested in getting behind this cause, you can still donate to support BFAC here.

Saturday, 20 May 2017

When Do You Feel Most Lonely?

This one is a fairly short one, but I thought I'd ask a question of people for once. When do you feel most lonely? Because the thing is, for me, I feel most alone in a crowd. That might seem a bit ridiculous, but hear me out.

When you're by yourself, you can't connect to anyone. You're by yourself. You expect to be alone, and you are. And you get a bit lonely here and there, but it's not usually too bad.

But when you're in a crowd, when you're amongst other people - well, there's so many people to connect to! Surely, one of them will connect with you, right? Surely, someone will....no....oh, okay then....

That's why I feel most alone in a crowd, or in a room of people, or at a lot of events. Most of the time, I'm sitting or standing by myself, and everyone else is talking to someone. And I wonder what it is they've got that I haven't. How do they do it?

It's relatively simple, of course. They connect. They talk. They interact. I do that as well, but it usually feels a lot more - pointed, than it should be. It feels like it should be spontaneous and natural. But with me, it's more like a list in my head. "Okay, I need to talk to this person about this, and this person about that, and it would be nice to talk to that person," but inevitably, each of them is already talking. It would be rude to interrupt. But I don't want to just sit in one spot. I'm terrible at keeping still - well, I'm okay at it, but I like to move around. So I do, until someone is free. Then I hope I can dive in before someone else does....

That's not what conversation always is for me, of course. It depends very much on the context. The above is fairly typical for me after church, for instance. Not so much at my new church as yet, because I don't know anyone much well enough to talk to them! Guess that's the point of talking to them.....oh, yes, for those who haven't heard as yet, I'm at a new church now. Not because I didn't like the old one. I rather do. Just a bit of a new direction for a season - not sure how long a season. We'll see as we go. But at present, I'm leading the music for the evening service over at Cobbitty Anglican. Lovely old church. Very old, actually. Heritage listed. Beautiful building. Good people, too. Always nice.

Anyway. Yes. Conversation, interaction. All that sort of thing. Feeling lonely in a crowd. So. Not sure if that's just a me thing, or an Aspie thing, or actually somewhat broader. So thought I'd ask around! When do you feel most alone/lonely? Would love to get your thoughts :)

Wednesday, 10 May 2017

A History Of Septimus.

For a little while now, I've been working on a board game called Septimus. Most of it is done - the rules, the ideas, how it all works together. What takes time is all of the cards - I've got two sets of decks I need to make, one for Items, the other for Encounters. There are 70 Item cards, in two decks (of 42 and 28), and then 140 Encounter Cards, in four decks (of 14, 28, 42, and 56). I'm wanting each to be unique. I have a fair few ideas about what they'll look like, have them categorised, I've got a few examples of each....it just takes time.

But one thing I only wrote relatively recently, but had had in my head since near the start, was the history; the story of the game, the context. So I thought I'd share that here. History buffs will quickly realise I'm using a touch of Latin. The names, if you're interested, are mostly real. I think I only invented one. I'm not sure if I'd say the people actually spoke Latin; perhaps it is in tribute to their ancestors who did. More to figure out! But for now, read on, and discover the world....of Septimus....

In the land of Patriam, at the height of the Middle Ages, there arose seven charismatic and influential leaders. First, Seneca, a philosopher, a very wise and elderly man. Second, Ennius, who worked wonders with mechanisation. Third, Petronia, a fierce warrior. Fourth, Terentius, an expert navigator and sea captain. Fifth, Ignatia, who delved into the new field of explosives. Sixth, Maximilianus, an in-depth and disciplined researcher. And seventh, Untalia, who hid in the shadows, and worked in secret places. 
Each of these developed a faction around them, of people like themselves, who had their ideals and skills. And each went to war against the other factions. 
The fighting was long, and bloody. Each faction wanted leadership over Patriam for themselves; none was willing to concede. Even those that seemed to get along well, and had originally supported one another, turned against each other. The war went on for generations, with no sign of ending. 
Finally, Seneca stepped forward, calling for a council, with a member from all seven factions present. They believed that they had an idea for peace. Slowly, each other faction agreed, and the first Council of Seven was held. 
Seneca proposed that, rather than one faction ruling over the land, all seven could live together. Each year, a leader would be chosen from each faction, and they would compete to see who would rule for that time. After some discussion, the others agreed. They were tired of bloodshed. 
Ennius then proposed that this competition could take place in a maze with various encounters, which they would build. Petronia supplied their best warriors to test the maze. Terentius scouted out the best location to build it. Ignatia brought their pyrotechnic expertise to many of the traps. Maximilianus researched and tested to deduce the best encounters to trial the skill of each faction, and to make it fair for each one. Untalia advised Ennius on many of the unexpected surprises to be found in the Maze. 
At the second Council, they formed a joint government and law between the seven factions. Each was given, and was responsible for, a seventh of the land; as such, each faction was referred to, then on, as a septimus. Together, they were called the Septem Septimus. 
The Maze became part of the culture for each septimus, each preparing in their own way. Each septimus knew bits of what to expect, but none knew all. The Maze changed every time, and you didn’t know what you would face until you entered. But each year, each septimus selected their Hero to enter the Maze, to potentially lead the land for the year to come. 
You have been chosen as a Hero. You represent your Septimus. You face the Maze. Will you emerge victorious?

Saturday, 6 May 2017

An addendum to triangles.

Quite a while back, I did this post. In it, I made a bit of a boo-boo. And I didn't realise it at the time. I figured it out by finding this page here, looking at the same problem. I discovered quite quickly that I'd been missing out all of the downwards-facing triangles that weren't unit triangles. Which wasn't a problem for the first three triangles, because there aren't any. The fourth has only one. But then it goes up.

So, my previous formula of (x^3 - x)/6 doesn't work at all. So I tried to find a new one.

First, I tried doing it while maintaining the x^2 out the front. I discovered that the rest of the sum was the series (0, 1, 4, 11, 23, 42, 69....), which, when typed into the online encyclopaedia of integer sequences (quite handy), said that it was the sequence "A019298 - Number of balls in pyramid with base either a regular hexagon or a hexagon with alternate sides differing by 1 (balls in hexagonal pyramid of height n taken from hexagonal close-packing)." You can have a look here if you like. Unfortunately, it looks like they don't have formulas for the nth term in the series in any simple form, though I'm probably just reading it badly.

So I tried it a different way - separating out the upward-facing (which I knew was just a sum of triangular numbers, and was easy enough), from all the downward-facing. The latter yielded this series: 0, 1, 3, 7, 13, 22, 34..... which also came up, this time as "A002623 - G.f.: 1/((1-x)^4*(1+x))." I've just found out that G.f. stands for Generating function. Again, though, it didn't have any simple formulas.

There were formulas available for both. But all of them included extra expressions. They're all given in the format a(n)=, n being the nth number in that series, and a being that series. But then they'll have a(n-1)*a(n+2) in the formula or something, which isn't helpful! I need it just in terms of n. But, they didn't have that.

So, at present, I have no formula for this. Unfortunately. I knew you were all hanging on for me to pull out something nice, right, but I've got nothing for you. :/ If any of my maths friends can figure it out, let me know!