110 = Inventive Dice and Paperwork Advice

Hello and welcome to A Problem Squared, the problem-solving podcast, which is a lot like a Comic-Con, in that it exists entirely because of nerds, and I'm dressed like Wolverine.

That's true.

Your hosts are myself and Matt Parker.

Matt Parker is a comedian, mathematician, and YouTuber who is the big ticket guest everyone has come for.

And I am Beck Hill, a comedian, writer, and presenter who is the person who rocked up for the Hair and Makeup Convention one week early and is severely confused.

That checks out.

I did wonder why you're always dressed as Wolverine for these recordings.

Yeah.

Yeah, just a big hue Jackman fan.

Sometimes I dress as the greatest showman.

Sometimes I dress.

Plain clothes Wolverine, not like the costume or anything.

Yeah, I've just got a leather jacket and white singlet showing a lot of chest hair.

I mentioned the Greater Showman.

I've never seen it.

And I can't think of a third Hugh Jackman film.

That's enough.

And in this episode, I've worked out how to give reduced dice a fair shake.

I'm going to be changing history with some new words.

Oh.

And we have at the end of the convention the QA we know as any other business.

Excuse me, just wanted to say, big fan, big fan, exactly.

Wait, wait,

in episode nine, eight.

You know, you could pick any of our episodes at random, and there'd probably be a mistake in there.

Someone could pick out.

Oh, yeah, I know.

As a problem-solving podcast, this is very problematic.

Matt, how are you?

You're still in Australia?

I'm good.

I am probably

more dressed up in a costume than normal

and I will do the big reveal in a moment because now normally I wouldn't say something that listeners don't get to hear.

I don't like to tell audiences what they're not getting.

But we recorded a very brief chat last episode that got cut from the edit.

We talked about how I was going to a big gravel cycle race that I was looking forward to.

And we put it in the episode because it might be fun if other people were there, and I was very excited about it.

The very next day, I came off my bike and broke my hand.

So we had to go back and retrospectively take it out of the edit.

So we weren't telling everyone, hey, Matt's doing this fun thing, come and see me.

And so I didn't get to do the race.

The race has come and gone.

And I now have my arm

in a blue thermoplastic splint held together by by what I think the color can only be described as safety orange velcro.

Yeah.

And do you know what?

With your shaved head, you've come to this theoretical Comic-Con as Charlie's Theron's character from Mad Max Fury Road.

You know, not far off.

I'll take that.

You guys look like you've got a

mechanical arm.

You've got a plastic prosthetic arm.

Exactly.

That's probably painting a very accurate picture for all our listeners.

I've always said you look like Charlie Theron.

You have.

You have brought brought that up.

So I came off the bike, very

boring bicycle accident.

I wasn't even in training.

I was just cycling down a cycle path in suburbia in Perth.

And I looked down at my little cycle computer to see if I was going to make it to the cafe before they closed, just to check the time.

That's the most matte distraction.

The fact that you called it a cycle computer, I think, is.

Yeah, yeah, you know, the cycle computer.

The hipster cafe was still open.

Yeah, and it turns out the cycle path was about to end.

And what City of Sterling and their infinite wisdom decided to do, because the cycle path wasn't like

physically separated from the road.

It's just like a painted edge of the road.

And you're like, okay, I'll cycle in the painted edge of the road.

But when it ended, and they want to put you back on the footpath, they just put a curb in.

Like a super low curb, the top of which is the same color as the cycle path.

And so I just totally didn't even see it coming.

And I glanced down at the wrong time.

When I glanced up, I was ricocheting off the curb because the curb was there to kind of deflect you onto the footpath or something.

But not like a dropped curb, like proper height curb.

Yeah.

So they just curb.

Slapped in the middle of the road.

Now, I went and took photos.

I

so the theme of my photo shoot was Angry person complains to local newspaper.

So I was like looking sad in front of the curb,

pointing at my broken arm in front of the curb, all that.

So I'll supply a photo.

You can decide which one is the most like I'm on the front page of a local newspaper.

Okay.

Oh, would you like, do you want to see them now?

Mid-conversation?

Here we go.

Also, I want to see it, mid-conversation.

What are you talking about?

So true.

Hang on.

One second.

Oh, God.

Oh, God.

These are so good.

If you, you know what?

If you pick a good one, I will send it into the local newspaper and say, local man cycles into curb.

These are.

These are great.

Lucy should consider a job at the local newspaper.

The local paper photographer.

She did an excellent job.

So can I describe this for the listeners who might not have access to look at these online right now?

Yes, yes.

So what they've done...

Yeah, so they've built the dividing bit.

between the bike lane and the actual road where cars go is, as you say, a curb.

It is the exact same sort of reddish

colour that the cycle path is, which means it, even in the photos, it sort of looks like it could be flat.

And there's no curb the rest of the time.

There's just a painted line.

I've just massaged it.

Yeah.

Suddenly third dimension.

Right.

Yeah, exactly.

And then what they've done is they've just kind of,

you know, if you were playing with like matchbox cars and you just like.

wanted to divert a car off the side so you just like

chuck a slap a thing on an angle in front of it and then throw the car and imagine it just so that's kind of of they've done that as if cyclists are the same.

You're just going to go

and track on to the thing rather than that being severely confusing.

I actually do think you should send these into the local paper or at least send these into the council because this does actually look like

you just got on for the broken hand.

Yeah.

I mean I fully acknowledge I looked down at my Cyclotron 2000 at the wrong time.

I get that.

I was a distracted cyclist, but it did, it was, it didn't take much distraction to not see that curb coming.

Now, one thing that is different that you may have noticed about looking at these photos is I'm not wearing my funky thermoplastic multicolored splint.

No.

I'm wearing what can only be described as an 80s plaster cast.

Yes, you are.

Yeah.

Which I think you were originally fitted with.

Yes.

So when I came off my bike,

I initially just thought it was a big scrape on my knee that was the issue.

I really hadn't clocked.

I'd broken my hand.

So I,

good news, made it to the cafe before they closed,

got my coffee.

I then cycled to a chemist's and bought like saline solution and bandages to reassemble my knee because that's what I thought the major issue was at the time.

And it wasn't like deep scrapes, it was like normal

you've you know, scraped your knee kind of stuff.

It wasn't particularly serious.

That night, I was like, oh, my hand does hurt a little.

Maybe tomorrow I'll pop by the urgent care room to get it looked at.

And I woke up the next morning and my hand felt better, but did look a little swollen.

So I thought, you know what?

Out of an abundance of caution, I'll pop by.

It'd be kind of fun to get an x-ray.

I'll pop by and see.

And I pop in and I'm like, oh, I'm sorry to, you know, you know, it was classic.

I don't want to waste your time.

I'm very sorry.

My hand's a bit swollen.

I came off my bike yesterday.

I had the presence of mind.

I almost cycled over and i had the presence of mind to get the bus instead

and they're like oh okay well the doctor's gonna want scans so we may as well do the x-ray first then we'll send you through get all that done the doctor comes into like the little triage room i'm sat in and they're like oh um i just seen your x-rays uh so what have you got planned for the next couple weeks i'm like oh i've um doing this big cycle race in like three or four weeks and he just starts shaking his head and i was like, oh,

I was going to be doing a big cycle race.

He's like, that's better.

It's like, come with me.

And he showed me the x-ray.

And he's like, you've broken.

So I'm now showing back my good hand.

Yep.

And you've got the equivalent of the ring finger.

So I broke my left hand.

I'm showing my right.

You've got where the ring figure would be.

Your finger's made of like a couple bones.

And then there's one big finger bone that's basically inside your hand.

That's your metacarpal.

And it looks like a comedy bone, like a dog would have in a cartoon.

Long, skinny bone, bobbly end.

That's great.

The bottom bobbly end, I broke off.

So the break goes horizontal through the whole thing.

That's a proper break.

Side to side.

Proper, proper break.

I was a little miffed.

When they're like, oh, you know, they get you to rate your pain.

And I was like, I'm in no pain, really, to speak of.

And they put me down as a five.

So I think five is a guy pretending he's not in pain.

I'm like, genuinely, there's no pain.

I'm fine.

I think once you've been stung by an ant in the Amazon, you know, it's just.

Whereas women are like, I'm in a lot of pain.

And they're like, so are three.

A three.

In fact, we don't exactly.

I'm not painting this at all.

Go on.

Yeah, yeah.

It's like nine, out you go.

Yeah.

Yeah.

Medical people.

Anyway, yeah, so I broke them straight across the side of the bone.

Every medical practitioner I've spoken to has been very impressed.

They're like, great break.

Really nice.

Yeah.

Straight across.

Just like tens across the board.

Yeah.

Yeah.

Yeah.

Oh, top-notch.

You nailed that break.

I'm like, I would rather have not broken it.

And they're like, great job.

Stop congratulating me on breaking my hand.

So, but it is, like, it's the best case scenario.

It's a clean, solid side-to-side break.

It's not

on the joint or anything.

So they basically treat it like it's a broken wrist because that it's the wrist end of the bone.

So technically, I broke my hand.

Functionally, I've broken my wrist.

And that big plaster cast, that was like

the opposite of bail.

It was like, it's to guarantee I came back to see

the occupational therapist to get a proper one done.

They

didn't trust me to come back.

I'm like, no,

this is attached to you until you come back I'm like

On the way back because I'm I'm in Australia Lucy hadn't come out yet I'd come to Perth Lucy was flying in a couple days later So I had to go home by other shops and buy all pre-sliced vegetables so I can make dinner

I Like how when you break your hand you still take better care of yourself than I do for

Like I picked up some cereal on the way home yesterday and was like mama's gonna eat for another day

And I'm like, oh, two types of pre-sliced mushrooms

I made pizza I made pizza I was like I can assemble a pizza with one hand I don't even make pizza you know

I got the pre-done base

and I made it all work Matt you just chuck them in the oven what oh but how will it get to my house yeah

no I still wanted to make something nice so sad Matthew could eat a pizza yeah so So the thermoplastic's amazing.

It's waterproof.

I've been able to go swimming in the ocean.

I can shower in it.

Underneath it, when I first got it done, they had like a compression band underneath.

What I'm wearing now in Australia, you can buy just the sleeve of like a sun-safe top.

Yes, and they've got a name.

I got given some as a freebie with something.

Yes, I wanted like they're a bit more comfortable if you've got something underneath them.

So I realized I could buy just the sleeve with a thumb hole off the internet.

So that's what I'm wearing underneath.

So I need to wear this.

I've been in it for a couple of weeks.

I've got to do six weeks in the splint and then another six weeks still technically healing out of the splint after that.

So 12 weeks all in.

But the last six weeks, I don't have to wear this anymore.

I just got to, you know, be careful.

Do you get, have you had the itchy arm yet where you have to stick a ruler down it?

Oh, I did when I had the plaster one on.

Thank goodness.

This one I can take it off.

I can, you know, take it off, wash my arm.

I just got to be careful.

I'm not allowed to do, and I'm demonstrating on my other hand for Beck, this, this action.

I don't know what you call that I guess if you were doing if you're knocking on a door without moving your forearm yes the door knocking action

no the the nodding fist action yeah

if I was a Muppet and it was the I couldn't say yes to anything that said the one exercise I have to do is no

So to stop there's some tendon or something, and it's the rotational, the two wrist bones going around each other.

So my Muppety friend has to say no three times a day, but I'm not allowed to say yes until six weeks in.

So that's that's where I'm at.

So

that's how I'm doing.

How are you back?

Well, listeners may have picked up that I sound, there is a bassiness to my voice, while also a nasal, nasal-ninness, a nasalness.

Yes, I co-hosted Brussels Comic-Con.

As regular listeners might know, I do that twice a year with with my wonderful friend Matt Highton.

The second match in my life.

Yeah.

And so

we were hosting it.

It was a lot of fun, but I got the

Comic-Con cold afterwards.

The nerd-lurgie.

Yeah.

The simultaneous cold convention that's coming on.

That's right.

Yeah.

So

I've just been dealing with that largely.

But it was a really fun, really fun Comic-Con.

Got to interview John Boyega, who plays Finn in Star Wars.

Yeah.

He is a delight.

He's a delightful man.

He's such a big fan of Star Wars.

It was probably like one of us.

He genuinely, to this day, is still thrilled that he was a part of it.

And it was really fun chatting to him.

He's very down-to-earth, very, very grateful for his career.

And I just found that very interesting.

I also got to interview Charles Martinet, who is the voice of Mario and Luigi and Wario and stuff.

That was very fun.

He's great.

So I got to go woohoo with the voice of Mario on stage.

That was very exciting.

And now we're all sick.

No, I don't know if they're sick.

I'm assuming.

The listeners better be extra appreciative that you've woken up fighting through a cold.

And I've got the operation of a single hand, but we're still here.

Putting in the podcast.

And if any listeners are like, why didn't you just do it on a different day?

We don't have time.

We push this right back to the last conceivable second.

Producer Laura is nodding, going, I've barely got time to edit this.

Our first problem comes from, yes, that old guy

is the name they entered.

No space.

I don't want to.

Yes, no spaces.

Yeah.

What did you say?

Camel Case.

Camel Case.

Yes, where you capitalize the first letter of each word.

Yeah, yeah, like a camel.

Yeah.

Oh,

I've never heard of camel case, and I love that.

I learned something new every day.

There you go.

What a wonderful thing.

What up this show?

See, long intro, but now we're making up for it already.

Yeah, look at all the education, you guys.

Right.

Yes, that old guy says, I'm designing a game using dice, but I don't want to use traditional dice.

I want three-sided dice, but that's not possible.

So I want to use six-sided dice, but with two ones, two twos, and two two threes.

This is my problem.

With a six-sided die, the pips on opposite sides, and I know now that a pip is the little dot on there.

I believe you told me that, Matt.

With a six-sided die, the pips on opposite sides add up to seven, which I think makes the die fair.

With my special die, I could do a similar thing with the ones opposite the threes and the twos opposite each other.

That would make opposite sides add up to four, but that puts the ones next to each other and the threes next to each other.

But if I put the ones, twos, and threes opposite themselves and the opposite sides add up to two, four and six.

Yep.

All that being said, it probably doesn't matter if I'm only rolling one die at a time, but in my game you need to roll three.

This is trying to get a bit cones of Dunshire.

Is it going to matter then which way is more and then in double quotation marks?

Multiple quotes.

Fair.

Thanks for a great podcast.

Blah, blah, blah.

Yours truly, blah, blah, blah.

How dismissive of you.

Skipping over.

I love love that people are picking up on this now and they're just adding blah, blah, blah.

Writing blah, blah, blah.

Okay, so here's the thing.

A normal dice, D6,

opposite numbers add to seven.

And that's pretty much, without only a few exceptions, all dice have this property.

If you get a D20, So 20 sides, 1 to 20, opposite sides add to 21.

Or if you get a D12, opposite sides add add to 13.

Opposite sides traditionally add to one more than the biggest number on the dice.

And the reason that's true, and this is kind of a nice way to think about it, is what you can do is, first of all, you put the smallest number opposite the biggest number.

So for the case of a, let's say, a D12, you put one opposite 12.

And then you partner the next smallest number and the next biggest number.

So then 2, which is 1 bigger, is opposite 11.

That's one smaller, which means they still add to the same thing.

They still add to 13.

And then you do the next one, one bigger, opposite one smaller, and they still add to the same amount.

And it's a really nice way to make sure the sum of the opposite faces never changes by just gradually making one number bigger and one number smaller.

And people

like this as a dice property.

What, yes, that old guy is worried about is that this is done

as some kind of deliberate property of dice to make them more fair.

And as far as I'm aware, that's not the case.

Now,

you can have manufacturing defects in dice.

So imagine you were trying to make a cube dice and you accidentally make it a little bit short in one direction.

So it's getting closer to being a chunky square, not a dice.

And you think, well, actually, that makes...

the numbers top and bottom of the direction where it's squashed more likely to come up because it's getting closer to flipping a coin than it is to rolling a cube.

And if, in theory, opposite numbers add to the same thing, you'll still get the same

average

out

because the opposite ones will be ones that balance each other nicely as such.

So you'll constantly get more likely ones and sixes, ones and sixes.

You're still averaging three and a half.

Or you're constantly getting, you know, threes and fours, threes and fours, you're still getting the same average value.

So there is an argument for that, but now manufacturing techniques are pretty good.

It doesn't really matter, to be honest, if opposite sides are the same.

I have two questions.

Yep.

One,

and I've always wondered this about dice.

The number is slightly debossed into the dice.

Yes, yep.

And obviously, six uses more than a one side.

Correct.

Yep.

Which means that technically the one side is ever so slightly heavier than the six side.

Correct.

Does that ever come into play?

It's a very, very slight difference.

It's been solved different ways.

Henry Segerman, fantastic mathematician, came up, I think it was him or either someone he worked with, dice where each number, so instead of doing pips, it was digits,

worked out a way that every digit has the same area to write it.

So it means you're removing the same amount of material from every face.

Love this.

Great.

However,

all mass is not equal.

How far away it is from the center, in terms of like inertia and things, it's the distance from the center of rotation times the mass.

And so another dice company based out of Sydney, I can't remember the name at the moment.

I'll look it up, put it in the show notes.

They did all the calculations so that their dice, because I think they were making them out of metal.

They compensated for the amount of mass missing different distances from the center of the face.

So people have gone to extreme lengths to solve that problem, but it only matters if you've got very precise dice.

And even then, I don't think it makes a difference.

It's such a small factor.

Yeah, because I just recalled that sometimes you get a die that has like a very big one, like the pip is quite large compared to the others.

And now I'm like, wait, is that for that reason or just

obviousness?

If you want to find out what you can do, and I've never done this, but I've heard this is what people do.

You can get a salt solution.

So keep dissolving salt in water until the dice you want to test becomes buoyant and then if you let it bounce to the surface a couple times you'll see which way up it floats and by if it always floats the same way up then there is an imbalance like it's slightly weighted but if it always bounce like if it floats whichever way you put it then actually it's perfectly balanced So if you're ever super worried about a dice shape,

someone in the Red Sea just throwing dice.

Yeah, yeah.

Find a solution they float in and see which way.

If they consistently float the same way, then yes, they're slightly weighted.

But I suspect it's very rare.

It's any, I don't think it would ever be an issue.

And if it is an issue, it would only be the slightest bias towards one region of the dice, let's say.

So actually, Henry Segerman, who I mentioned, who works with some people at the dice lab, Henry was designing a dice with 120 120 faces the D120

which is the most faces you can have

on a fair dice before you resort to making like a roller or a spinner or something else

and for that they Henry was thinking ah I want to make sure if there's any slight imbalance it's not going to be a specific face but it'll be more of a region So what you really want are just general regions are equivalent.

So you get a property called numerically balanced, which is if if you pick any one corner on the dice, all the faces around that corner, vertex, add to the same thing.

Okay.

That's what you want.

As opposed to being opposite faces adding to the same number, you want each vertex to have the same sum.

That's called a numerically balanced dice.

A guy called Bob Bosch actually did the mathematics to work out the arrangement for the 120.

Most D20s don't have numerically balanced arrangements, although Henry did find one for the D20, which we sell on Mass Gear.

It's on the dice lab as well if you're in the US.

That exists.

Link in the show notes.

Link in the show notes.

A couple years ago, I got interested in this

because you've got these two properties that people want in dice.

One is that opposite sides add to the same thing, and one is that numbers around a corner add to the same thing.

And I realized of the 15 ways

you can have the numbers one to six on a dice.

There's only 15 options.

There's the one we use where where all opposite faces always add to the same thing.

That is the worst case scenario.

That's got the worst distribution of vertices being balanced.

If you find the one with the best vertices being balanced, it's got the worst opposite faces problem.

So what,

yes, that old guy is basically asking

And he hasn't articulated it this way, but he's worried about having numbers that are the same number next to each other, which means they're around the same corner.

He's like, oh, is that an issue?

Because now you've got lots of similar values near each other on the dice versus have you got opposite faces that add to the same thing.

So it's a very interesting question that, yes, that old guy has come up with.

And to work it out, I went and actually I couldn't find my old spreadsheet because I did this like eight years ago.

I recreated my old spreadsheet for normal D6 and then I swapped in the numbers so it's just one, two, three, one, two, three, and re-ran the calculations, and it's exactly the same problem.

It's different arrangements, so it's not just people just thinking we just do mod three, it's different for anyone thinking that.

It's different ones, but once again, the arrangement that's best for opposite faces is the worst for corners, and the one that's got perfectly balanced corners is the worst for faces.

So, you again have to decide which way around do you want it.

Are you about to solve this?

So, one answer is: yes, it is a choice you have to make.

You look like you've got a question.

I had a second question.

Oh, of course.

We skipped over.

We have a lot of fans of Clojure that listen to this, and they're very upset that you started a number list of two things, and we did exactly one of them.

So,

you know, I was never going to leave.

I've been waiting very patiently.

I was wondering.

I'm like, Beck's got an

unfinished business look about her.

Okay, good to know.

What is it?

Where do dice come from?

Where did we start?

Did you never have the chat?

Yeah, yeah, I've never had the chat.

I mean, the D6s we know and love has been around for a very long time.

There were Roman dice were found that are D6s, as you'd recognise a modern dice.

So

they're not new.

But in terms of where they come from.

Were they for games?

I guess there was a lot of betting games with dice.

Yeah, now this is outside my field of knowledge.

Obviously, games and betting.

are if I had to guess number one games humans have been playing games since prehistory and dice randomness in games big thing, which is why we found dice and things that people there's like Neolithic stones people think might be dice, but I'm not convinced.

Then separate to that decision making like often and this is outside my field of knowledge if you want to know the wills of the gods you assume the gods control randomness you draw lots you do something random, and through that random uncertainty is where the deities can communicate their wants.

So I wouldn't be surprised if also DICE came out of a tradition of using randomness to make decisions for whatever reason.

That's a problem to be solved in the future.

Is that the conclusion of the list?

That is the conclusion of the list.

Before you solve this problem, I think I have a solution, and I don't know whether you would like it before or after your your solution.

I would love it right now.

I think get rid of the D6 idea altogether.

Oh, okay.

Yep.

Gone.

I think you want to make, and I'm sure there's a better term for this,

an isosceles pyramid.

I can guarantee there's a more precise term, but none better.

Like a triangular, like a three-sided pyramid.

What's that called?

Is that still a pyramid?

Or is it pyramid specifically four-side?

I know.

A pyramid can be any base.

But a triangular-based pyramid.

Triangle-based pyramid.

We would call a tetrahedron, would be the name of that shape.

But triangle pyramid, perfectly valid.

It's called a tetrahedron because it's got four faces: the triangle base.

Yes.

And then the three triangles that come up.

So you want a tetrahedron where it's quite long and pointy.

So, you know, like a Christmas tree.

You've got to go to go.

Yep.

Yep.

And then on

your little base side,

you want, which would actually be an equilateral triangle on the bottom.

Correct.

Well done.

So it looks like an isosceles when it's standing up, but when you look at the base, it's an equilateral.

And then you have one, two, and three on the corners.

So when you roll it, one of those corners is going to be up, and that'll be your one or your two.

Just the one.

That works.

That's my solution.

That's a good solution.

The regular tetrahedrons uses a D6, but it has the same same problem that when it stops moving, there's not a face at the top.

It's a pointy bit.

And you could do the same thing with, it wouldn't have to be pointy.

It could be like a triangle prism.

So it could be a long, like a Toblerone box, like a long triangle prism.

Oh, yeah.

Yep.

And again, you do the same thing.

You'd have one, two, three in the corners on the ends, and whichever ones at the top.

When you roll it, works.

100%.

The actual practical solution to this, and this is true of most dice-related things, is a roller, which is what you've just described, where you have as a prism or a pyramid with as many faces as you want to be, you know, one to whatever, and then you roll it, and it's the top one at the top works, or you have a spinner, which is the classic.

You spin a thing and it spins around.

Yeah, like Wheel of Fortune.

Like Wheel of Fortune.

No, it's just really like rolling a regular polyhedron.

Yeah, there is a clunkiness to any tetrahedron-style dice.

Yeah.

If it was just about getting a random number, spinner.

Or a roller.

Like it's a big chunky cylinder.

With multiple faces.

You get what I'm saying.

But the dice, the dice, there's just something pleasing about the dice.

And a cube is such a nice, easy thing to make and roll.

And it's unambiguous when it stops rolling.

So I get it.

Now, the actual problem is it doesn't matter.

Within the tolerances of what you're doing, it doesn't matter.

Just buy a normal dice.

You got one two three and then four five six take them as one two three again boom piece of cake it's either the number you see or subtract three done

if you really want to get into the maths of it which i believe some people probably do

there's a few more options than we were led to believe there are the two cases that were mentioned there's the one case where Every number is opposite itself.

One's opposite one, two opposite two, three opposite three.

You've also got the case where no numbers are opposite themselves.

That's where, like, one and one are next to each other, two and two are next to each other, three and three are next to each other.

The best case for vertices is where everything is opposite itself.

I mean, to recap, best case for opposite faces, two is opposite two, but one and three are not opposite themselves.

Best case for vertices being the same as when everything is opposite itself.

And the in-between cases give you different combinations of the two.

And there's actually only two sub options within that.

Your sub-cases,

you've got the other two cases where three is opposite three, but one and two aren't opposite themselves.

And one's opposite one, but two and three aren't.

They all make the vertices slightly worse, but the faces slightly better.

It's still biased towards the vertices being the most balanced.

but it's a bit more equal between the two.

And then you've got the cases where nothing's opposite itself.

And that

is

very close to the opposite faces being the best, but they're slightly worse and the vertices are slightly better, but biased towards the faces.

Could you clarify again what vertices and faces mean?

Because I've gotten confused and forgotten what ones watch.

Here's the whole list.

You've got one option where opposite faces always add to the same thing, but if you add the numbers around a corner, they're a mess.

Okay.

You've got the other extreme where if you add the numbers around a corner, perfect, always sum to the same thing, but opposite faces

nightmare.

And then you've got two options which are along the spectrum.

You've got one where opposite faces are pretty close to always adding to the same thing, but not quite.

And the vertices are less of a mess than they could be.

And you've got the one where vertices almost always add to the same thing, but not quite.

And the faces aren't quite as mess as they could be.

So there's your four categories.

It makes me think of like those graphs where you'll have like the X and Y axes as like better for vertices, better for faces.

Agreed.

And then you can position that in the four or combinations of them.

Agreed.

And I'm sure someone in Discord will whip that up.

Yeah, 100%.

And thank you in advance.

And my spreadsheet was pretty quick and dirty.

I didn't go through and remove duplicates.

I just looked at how many different options there are.

But what you could do, the final solution I would say is, to be honest, it doesn't really make a difference.

I've just used an off-the-shelf D6.

If you were going to make your own dice, I would have

one of each different option, and then you pick a dice at random.

So use randomness

to decide which of the dice you're going to roll.

Just grab one.

What did they say?

Three at a time?

Yeah.

It's annoying there's four categories.

If there were three categories, that would be problem solved.

Roll one of each.

Ah, that would have been delightful.

Sadly, the universe does not giveth on this occasion.

So, I mean, it depends what you want to do.

I would say just use normal D6.

If you're going to go nuts, though, maybe do one of each type, and then people can pick three at random.

That's my solution.

My solution is file down an ice cream cone so that it's got flat sides.

Agree, yes.

I think, yes, that old guy is going to hate that answer because

with these sorts of things, we want a very clear, like, surprise.

It turns out there is a correct way with that.

Yes, yes, that would be lovely.

But I thoroughly enjoyed the journey that we went on.

I am fairly certain that this is not all we're going to hear about dice now.

I feel like we're going to get into a whole bunch of problems and we're going to get to do a bunch of deep dives.

Oh, my gosh.

Because

that's very exciting.

And I have a whole jar of.

Remind me: is it die for singular or for plural?

Now, my motto is never say die, but people get very upset about that.

So

your mileage will vary.

Depends if you're an angry pedant.

I don't think die is a valid word anymore.

I use dice.

But some people, that's the hill they want to dice on, and that's fine.

But in all seriousness, I always get them mixed up.

When people say die, do they mean singular or plural?

When people say die, they mean singular.

Okay, yeah.

Like how the singular of mice is my.

Exactly like that, yeah.

Yeah, cool.

I think all dice should be called douse.

One douse, several dice.

I'm going to give that a D,

which is a singular ding.

A singular ding.

But let's see what, yes, that old guy says.

Our next problem was sent in by Fred Rosenberger, who went to the problem posing page, typed in their full name.

Oh, and if it sounds all familiar to Patreon supporters, they have sent sent in a wizard problem that we did on the I'm a Wizard bonus podcast for the fine Patreon supporters who fund this whole enterprise.

And if you want extra extra podcasts from us of a lower quality...

I don't know.

I think it's funny.

I love it.

Patreon.com slash a problem squared.

Anyway, Fred here needs a new word created.

So Fred does a lot of paperwork, and they say it's always done on a computer with no actual paper involved.

Fred wants to know, what is a better term for this.

Bec, what do we got?

Computer work.

Computer work.

Job done.

Thanks, Fred.

Ding.

Now,

obviously we've solved Fred's problem.

For completeness.

Should we just explore to make sure we haven't missed a better word than computer work?

Because computer work, just

on my first hearing of the word, could mean other things.

Fixing a computer,

building a computer, doing something different on a computer that's not paperwork-related.

Arguably, paperwork could be a professional origami artist.

Origami, paper airplanes.

Yeah, yeah.

I do a lot of paperwork in my comedy or the flip charts.

Yeah, yeah, the thing I'm actually known for.

Yeah, I should do a show called Paperwork.

Why haven't I done that?

Paperwork.

Yeah.

Yeah.

Do you think the Pope does papal work?

Papal work, 100%.

Yeah.

Yeah.

If the Pope isn't saying that I've got a lot of paperwork to do, then we need a new Pope again already.

Get a better one.

The new Pope studied maths.

So.

Oh.

Now, I'm not saying all mathematicians are hilarious.

So, paperwork.

I mean, that was born out of the work was done on paper.

Yeah.

I do relate to this.

I refer to it as admin because...

I have to fill in a lot of forms.

The thing is, and we've mentioned this before, comedy, whether it's doing stand-up or

I'll extend it to YouTubing or podcasting or writing, right?

Or anything that's sort of within that

realm.

So much of it is not what you

hear or see.

Like, so much of it is

admin, is working out schedules.

Yeah.

or driving or booking train tickets, putting, like, there's so much work around it i mean

i

i tend to just say admin i do like to add to sometimes i say madmin uh right

if it's like it's chaos it's madmin yeah when i'm doing it with friends i call it ladmin

around with the lads ladmin and then yeah when i do it it's sadmin i don't want to be doing that

No, yeah, that's true.

At the moment, it's sadmin for me.

Yeah.

Badmin.

Badmin.

That's when you're doing it about shuttlecock.

Yeah.

I feel like admin is subtly different.

I feel like admin,

the act of, and this is a good example, booking trains and hotels and logistics.

I wouldn't call the analog version of that paperwork, though.

That's like planning an admin.

Paperwork has a certain archival aspect to it.

Like, oh, I've got a bunch of paperwork to do because things have to be put in places and sent or filed or whatever it is.

You're correct, yeah.

In fact, I used to work as a temp at the Edinburgh City Council and my job was to,

people would bring in their

paperwork to apply for a skip outside their house.

And I would have to check it to see if it had been approved and stamped and then give them the paperwork they needed to take to a different department.

That's paperwork.

Yeah, yeah.

So yeah, lots of, I guess, signatory type things, as you say, filing things, checking legal documents kind of stuff.

Yeah.

Yeah.

PDFing might be the closest thing we have these days.

Ugh, got some PDF work.

Yeah.

It's not good.

It's not a good word.

No.

I'm just exploring the space here.

No, that's fine.

That's fine.

There's no wrong answers.

No wrong answers.

Just terrible ones.

It's very bitty, and bitty is kind of fun because now we store it in bits as a

call back to our previous conversation about bits and bytes.

Yes.

Very

bitty work.

Bit work.

Bitty work.

Bitty work.

I feel like it's better than PDF.

PDF work, but that was a low bar to get over.

What does PDF stand for?

Portable document format, I think.

Producer Laura will fact-check that live.

Now, what producer Laura is doing right now is admin, but not paperwork, I would say.

And I'm getting the nod of correctness.

Excellent.

Excellent.

I think it was back in the day like a proprietary format, but then it was released.

Like it's open now, anyone can use it.

There's no restrictions around it.

Maybe we should just give it a totally different word that doesn't even suggest what it is, like

Svenning.

So

I recently learnt the word stoozing.

What's stoozing?

What is what do you think stoosing is?

And it's clean for this family-friendly podcast.

Okay, because I learned a new word recently in Dutch, and it's not clean.

Yeah, that's the Dutch for you.

Stoozing is the act of getting a credit card that has like a free introductory offer or whatever, maxing it out and putting the equivalent money into some kind of high-interest account to try and game the system to get free credit over here and make interest on it over there until you've got to pay it back.

It's dangerous because if you mess up, you'll lose way more money than you're making on the side.

If you hit the interest, ridiculous interest on the credit card, you're in big trouble.

But people have like complex spreadsheets to track their stoosing when they're trying to get cheap or free credit from one place and then try and earn interest on that money somewhere else.

Stoosing.

But it's named after, I believe, I looked into this, like the username of someone who suggested the practice as a hobby on a forum somewhere.

So the name is meaningless.

There's no insight from the name.

Right.

Because I was going to say maybe we should, in honor of Fred Rosenberger, I was like, maybe if I take the beginning of Rosenberger and the end of it, we can get like Rogering.

And then I was like, nope, that's a terrible idea.

I've got some Fred work.

Froger.

I feel like the answer is right in front of us.

It's now Burger Work.

Oh, I've got a bit of Burger Work.

It does sound like, Burger Work does sound like you work at McDonald's.

Yeah, you're right.

We're back to computer work.

No, I hear you.

Rosen.

Rosen's pretty good.

So then if Rosen was like online paperwork, a Rosenberger would be where you just got, you're just surrounded by Rosen work.

Put it in a sentence for me.

Oh, today's been a real Rosenberger.

Oh, yeah.

Yeah, yeah.

You know, I've got so much Rosen.

The Rosen is Risen, and I'm not staying on top of of my Rosen.

I got Rosen work up to my eyeballs.

No, okay, okay.

I can see it's not catching on.

Fredman.

Fredman's pretty good.

It's not Admin.

It's not Admin.

It's Fredman.

I think.

Frack.

You've got to go do some frack.

Frook.

Frack.

Frook.

Are you frocking hard or hardly frockin'?

Yeah.

But the thing about paperwork is visceral is not quite the right word.

But back in the day when it was paper, paperwork just conveyed its work.

And there's just paper everywhere.

So

the sad thing is, the sad min about this is we had a really good word that really conveyed the experience.

And now

We've evolved away from that meaning of the word and we need another word that conveys what a slog it is.

Well, I think maybe you've hit the nail on the head there.

It's paperwork without the paper.

So is it like work?

Sans paperwork.

Sans paperwork.

Paperless work.

Paperless work?

I like that.

Aperwork.

Aperwork.

Yeah.

Aperwork.

I don't know, it's just not quite paper.

No, I see what you're doing.

I see what you're doing.

Well, maybe we throw it open to the listeners.

I think that, do you know what?

I love a completionist thing.

But I, look, I'm not firing on all cylinders.

I'm still recovering from this cold.

Let's revisit this.

And this is one of the rare opportunities where this will come out before we record the next episode, I believe.

Oh, yes.

Because we're cutting it so fine on this one.

Yes.

So tell us what you think paperwork done on a computer computer should be called.

I will go away and have a think about this as well.

I'll chat to my friends, discuss it on the Discord, discuss it on the Reddit.

Reddit is a good place for this, actually.

Maybe I should specifically ask people to talk about this on Reddit so that

our problem-solving page isn't inundated

with Reddit.

Yes.

I mean, people can submit it that way, but we're going to get a lot.

Which is fine.

It's just more admin for Laura.

Also, if you're doing it on Reddit, then we can look at the things that have been upvoted the most.

That's true.

Yeah, yeah.

You decide amongst yourselves.

Great.

Let's revisit this.

Same time next time.

And in

any other business,

Insert Comic-Con reference here.

Do you want?

I realize that listening back to our episodes, we so rarely say that any other business, like the AOB, is just us talking about stuff we've talked about in previous episodes.

yeah we should make that clear they're gonna be like what the heck are they doing

yeah we're doing any

other business like what the heck are these people doing

any other brussels comic-con which is where i'm yeah see yeah yeah classic right what do we got uh this is from i dash van oh they posed the problem as an e-y-e-v-a-n thing that specified because we weren't sure if it was ivan or ivan Ivan.

Ivan.

It's probably Ivan, but

Ivan.

We've overshot.

Ivan.

Ivan.

We're still mispronouncing it.

Posed the problem in 107

about the number of megabytes and gigabytes.

Yep.

And they said, hi, Bec and Matt.

Thank you so much for looking into my problem with megabytes.

This is exactly how I imagined scientists would behave on both sides.

Yep.

I'm very satisfied with your solution, and I now have a great fact to bore people with at parties.

Ah, job is done.

I have sent you a M-D-I-N-G via Laura.

M-ding.

Great.

I will let you count them for yourself.

And there is a link here to a spreadsheet that Ivan has created

where every cell possible has been filled with a ding.

Thousands.

Or 1024s.

Yeah.

We get a few people send in

comments about when we in episode 108 discussed how you would prove a photo or some knowledge or a thing you did definitely happened before a date the opposite of the taking a photo with a newspaper example and I want to share one that was sent in by mean M-E-N-E

and they found a historical example so they'd like to point out that before hash was a thing which is what I talked about for my solution Scientists had other ways to do something similar.

So I just described, I like tweeted the hash of something I discovered because I knew I wouldn't announce it until much later in the year, but I wanted to prove I'd found it much earlier.

They said that Galileo in the year 1610

looked at Saturn with a brand new telescope

and thought he'd discovered something strange.

Galileo thought that Saturn was made of three pieces.

That's exciting.

I mean, I guess, well, I guess it's got a ring.

Does that count?

I don't know.

Anyway, Galileo thought they discovered something.

They knew they wouldn't get to publish this detail until they wrote a book a long time from now, but they wanted to signal that they had discovered it.

So they put out a little bit of text which looks like

gibberish.

It's just meaningless characters.

But it was an anagram.

So it was an anagram of a Latin expression that meant, I have observed the highest planet triform, or I've seen the highest planet is in three pieces.

And I don't think anyone could reverse that anagram into a meaningful,

because it was a weirdly worded phrase.

I don't think anyone could like meaningfully reverse it.

But afterwards, they can say, ah, you can see this was an anagram of a weird sentence that

conveyed this discovery to prove that I did it first.

So good suggestion.

It's not a planet made of three parts.

So do you think he was like,

oops?

Oh, that's not what it means at all.

Oh, I meant.

And then he's trying to create

three times.

Yeah, exactly.

He's looking for a different anagram.

Wait, wait.

It means I have.

Yeah.

So anyway, I like that.

Old timey.

If you want an old-timey hipster version of hashing something, anagram, a weird phrasing of it.

And on that note, we did hear from Daniel, who sent us the original problem about how to prove a photo from the past.

Yep.

And they wanted to give us a ding.

They said, I've also submitted the five unique words for Wordle problem three years ago and they never said a ding.

Wow.

But given that Matt got three YouTube videos about it, I think it's safe to say that's a big old ding.

That's so true.

Oh, that's great.

Daniel, thank you.

Daniel.

Wow.

Amazing.

Yeah.

Commitment to the bit.

Love it.

It's in my new tour show too.

So yeah, check that out.

Thank you, Daniel.

You get one free ticket, Daniel.

Send me an email.

We want to thank everybody who listens, sends in problems, or just tells their friends about the show.

You're the reason we do this.

But the reason we can continue this is because some of you who are in the position to give us money, and we really appreciate that.

So a massive thank you to our Patreon supporters who make this viable.

We'd like to thank you by giving you a bonus podcast, which Matt...

previously mentioned.

And we'd like to thank three of you at random at the end of every episode by mispronouncing your names.

And on this episode, those people are our

oblay

fertz.

Lou

is

on.

Well done.

D

and I eel.

And I'd like to thank my wonderful co-host, Matt Parker, who I wish a speedy recovery with your hand.

Thank you.

Thank myself, Beck Hill, wish myself a speedy recovery with my cold.

But most of all, I want to thank our fantastic producer who hopefully has managed to make me sound not as disgusting so that this is listenable.

Good luck.

Our producer, Laura Grimshaw.

who is the

handler,

which is the person who like takes the guests around and makes sure that they get to their like QA's and photo shoots on time and stuff like that.

I think Laura is our handler.

I thought you're doing a broken hand joke.

Thanks a lot.

Oh my gosh, double.

Oh, okay.

Yeah, no, that was totally intentional.

Well done, me.

Bye.

All right, I'm gonna go for E4.

E4?

Yes.

Miss.

Oh!

You've narrowed it right down.

Now, Beck,

last go,

I sunk your battleship, one of.

You did.

But curiously, I sunk it after six hits in a row.

And there are no battleships that are six long.

I was hoping you wouldn't realize that.

It means.

Of course, I noticed this.

I must have caught another ship along the way.

So,

to that end, I'd like to fire a shot at H7.

H7

miss.

Oh,

interesting.

Okay.