116 = Guess The Right Price and Why Teeth Might Splice

Hello and welcome to a Problem Squared, the problem-solving podcast, which is a lot like IKEA Furniture.

Oh, Beck.

You send us the pieces and we'll put them together.

Oh, my goodness.

That laugh is coming from my co-host, comedian, mathematician, and all-round

Billy bookcase of a man.

I'll take that.

I'll take Billy Bookcase of a man.

You're a Billy bookcase because you're tall and you contain a lot of information when being used correctly.

Yeah, yeah.

And I am your other co-host, Bec Hill, a comedian, adult tooth fairy.

And if I was Ikea Furniture, I'd be a particular type of light fitting called the Farti G.

I'm pretty sure it's pronounced Fartig, but I'm going to go with Farty G.

Farty G, right.

Because I am the original Farty G.

You are.

Yeah.

The oh farty g yeah yeah

so the reason for that intro we'll get into shortly but on this episode i've calculated when the price is indeed right i'm i'm talking about teeth i'm talking about teeth again wow

really distinguishes it from all the other episodes yeah and we've got some any other

I've already used Billy and bookcase.

What's another IKEA Ball as in meat ball?

Any other ball meatness?

Borg.

I bet Borg's one.

I bet Borg's a thing.

Blurg.

Any other blurgness?

So, Beck, do you want to tell us why?

Why you had an IKEA-themed intro?

Because we did the aforementioned on a previous episode, IKEA Wars show.

We did it.

We did it.

It was fun.

For people who didn't hear that episode, Beck and I are both, we're recording this live from the Edinburgh Festival Fringe.

We're both doing shows.

And in the lead-up to that, you can see that.

When Matt says live, by the way, like, no more different from when we're live elsewhere.

There's no one in front of us.

This is

not a live recording.

Yeah.

No, we're just sat in the living room.

Yeah, there's no audience here.

No, but we're alive.

Yeah.

Wow.

We take the pizzazz out.

I just don't want anyone listening going, oh, wow.

I could have seen it.

Now, that's an interesting point because

when you perform and do a show at the fringe, you want to do guest spots or things to help promote the show.

And in a previous episode, you suggested we both do a show called IKEA Wars.

We both signed up and we found out mid-recording that we were accepted and we were both going to be on the same episode.

Well, the same show, the same evening.

Yeah, episode.

Episode.

That's what they call them.

Yeah, so you and I competed against one another to put together a small IKEA trolley.

We didn't know beforehand if we were like a team, if we were in competition.

I mean, it's got the word wars in the title, so we figured it might be a competition.

Yeah, yeah.

And we took it seriously.

We did.

It was fun.

There were some sabotage options.

So the format is

that

two comics compete to see how quickly one of them can put together a piece of IKA furniture, but each member can also choose three sabotage options, which like cards, which can be played throughout.

the time whenever you like.

We're given an array of options.

This is what I find is so entertaining because a lot of you listening were in the audience.

We had a mouse full audience at past 11 o'clock at night on a Sunday.

Oh my gosh.

It was very much a home crowd.

It was lovely.

And as the host Kieran Bullock was explaining the sabotage options, one of them was socks for hands.

And so you can get your opponent to wear socks for four minutes, I think it is.

Over both hands.

And that got a very big laugh.

Yeah, a surprisingly big laugh.

Because that is a callback.

But we found that very funny because you have had experience

doing things with socks.

I had socks on my hands because I forgot my gloves and I was cycling in London during winter.

Yeah.

So I was like, well, I'm not going to choose that sabotage to play on Matt because you have had practice.

I've already proven I remain capable with socks on my hands.

But you threw me because as soon as we started, I dropped one of the screws and you played that card.

I've taken socks in your hands.

I'm like, bam.

And then that was the from there on.

It was a.

I got an early head screen.

I spent so long trying to pick up screws.

I heard a noise and I I turn around and Beck's like staring at the floor and there are screws on the floor.

And I say, Beck, did you just spill all your screws and bolts?

And you're like, yep.

And I'm like, sock time.

It was the worst time.

Like trying to get tiny screws into holes with socks on your hands was so difficult.

I considered using my mouth several times.

But then I remembered that this furniture has been taken apart and putting back together by someone.

Multiple times.

Yeah, yeah.

It's the same furniture every day.

Yeah, you played that.

I played T-Rex arms, where for four minutes.

I had my arms strapped to my body in a T-Rex position, and you had to do dinosaur sounds, yes, which I would like the record to state I did throw myself into, yes, but it was really fun, it was really fun.

And then you and I had a really fun as Kimeron was selling his stickers afterwards.

You and I were like, Should we deassemble?

And we did it like two kids who were being naughty, but we were just hoping staying back after class.

I think most comedians go out and like hand out flyers to the audience or promote their shows, whereas we're still on stage,

doing our shoddy work i just wanted to know that i hadn't lost all the screw i wanted to make sure we had all the pieces for tomorrow yeah it was a lot of fun so we're doing our own shows they're going fine yes yeah that'd be nice and i just want to shout out everyone who's come along to my show so far and said hi afterwards it's been really great seeing everyone and oh what i've loved the most is the is how many people have gone as i'm chatting to them i'm a big fan of problem squared blah blah blah

one of my favorite interactions.

So, after the show, I'm in the, I'm just in the courtyard where there's lots of like bars and food vans and stuff.

Yeah.

And we have like a line of people.

You, you all form a nice, neat, orderly line.

I'm very impressed.

So, my favorite moment was I was chatting to someone, and between people I was talking to, someone did a flyby blah, blah, blah.

So, behind me, someone just walking behind as they, as they passed within earshot, this went blah, blah, blah, and then ran off.

And I was like, oh, okay.

That's a good

fan.

Great.

That was it.

And then they're off to whatever they got to do with their life.

Yeah, that's great.

Thank you, whoever that was who did a

walk-by blah blah blah ring.

I do love a drive-by compliment.

Exactly.

Hey, you're great.

Yeah, yeah.

Oh, sweet.

Because I always think of when we were in New York and recording as we were walking down the street, and the guy just walked past and went, I love your content.

Our first problem comes from Calc Dave.

Or one word.

Yes, C-A-L-C-D-A-V-E.

Either that or Calc Dava.

Calc av.

Oh, yeah.

We could do this all day.

We have, but we'll keep the sticking along.

Calcedave, however you pronounce it, went to the problem posing page at a problemsquared.com, selected problem,

and asked,

how does adding prices right rules affect the best strategy for for guessing?

Let's say there's an item that I have no clue how much it is worth, but it's in the zero to 100 range.

Without the prices right rules, I think guessing $50 would be the best strategy for the first person to try and get closest.

But if you have to not go over the amount, should they guess a lower value?

I'm a day one listener and I've never missed an episode.

Thank you for helping people solve their problems and keeping me company on my runs.

Blah, blah, blah.

Back out of the blah, blah, blah.

It's like now we have to specify

blah blah blah in these scenarios

I like this problem already yeah I'd forgotten what the prices right rules were because we had that in Australia we did have

yeah that's the one I thought what we could do back just to establish how this works is have a quick round of the price guessing game for a price right so producer Laura here has found some items I believe

what website did you end up using Laura where are we guessing prices from We are going through the Argos catalogue because I've just moved house and it's proving very useful to me.

So I figured it was a good place to be available.

Other websites are available, but this one felt like a good mix of everything.

Brilliant.

So here's what's going to happen.

I don't know the prices either.

Producer Laura is going to show us a picture of something from the Argos catalog.

Americans, if you're not familiar with what Argos is, it was like Amazon, but they used to just print out the whole website in a book.

Yeah.

And then you'd order from the book.

Yes.

And you can go to the store and it's just a counter.

There's no display.

It's a warehouse with a counter at the front.

Yeah.

You type in numbers and then they bring you that product.

Like I can, but without the maze.

That's the one.

Or the meatballs.

Balls meet.

Now,

now, whoever gets closest wins.

You have to guess the nearest whole currency units.

We'll be doing it in pounds.

Okay.

And if you go over, you lose.

Would you like to guess first or second on this first round?

Ooh.

Second.

Second.

Okay.

Whoever goes first describes the product.

I think that would be helpful.

If you want to play along, we'll put these on socials so people can check them out.

Okay.

It's supposed to podcast if you want to bring up the picture.

Okay, what do we got?

Okay, so we are going to start with the Dyson Supersonic R hairdryer with diffuser in ceramic pink.

And there is a picture for you.

That's a funny product for you to have to guess, Matt.

Ooh, okay.

Piece of pipe.

It's a pipe with a resistor and a fan.

It's a glorified resistor.

How expensive can it be?

It's a curved pipe, and it does come with some accessories.

Oof.

I reckon that's going to run you 45 pounds.

There's a whole pound.

Oh, Matt.

Oh, come on.

Poor naive little Matt.

I've not gone over.

That's true.

I'm going to go minimum 150.

Whoa!

All right, okay, what is it?

So, this is the most expensive hair dryer that Argos sells.

Oh, my goodness, and it will set you back £449.99.

Oh, my goodness!

No!

At that price, it better give me hair.

It's giving her

so ridiculous.

Oh my goodness.

Okay.

All right.

Let's do another one where Beck has to go first.

Okay.

We are looking at some VTech Toot Toot Drivers Two Car Racer Pack.

They are some funky little toy cars.

They've got fun.

They've got little faces in the windscreens.

I feel like VTech, they tend to do those kids' computers and stuff like that.

Oh, you think there might be like

fancy electronics in these?

Maybe, but i'm i'm gonna go like i don't know 15 bucks okay 15 quid

now here's the thing i suspect they're probably a little bit less than that i'm gonna guess one pound not because i think they're one pound but i think they're less than 16.

and by saying one i can't accidentally go over

i see

uh so currently argos have them in their sale so the vtec toot to drivers i just want to say that again vtech toot toot drivers two two-car racer pack is currently £13.60.

I was screwed by the sale.

Yeah, because the pre-sale price was £17.

Oh,

so close.

You could have had it.

So close.

Oh, my goodness.

But you could have guessed 16 and you would have been fine.

Okay, given we've done one each, should we have a toe break?

Yeah, that's it.

Okay, whoever gets this wins.

And I'm up first.

Okay, what do we got?

And we win all the prizes, right?

Yes, all the prizes.

You get a really expensive hairdryer and some toot-toot drivers.

And

for round three, a Vilida 50-meter sunrise outdoor rotary clothes error.

So this is a four-armed rotary washing line that you stick in the ground.

Oh, okay.

Yeah, it is like a folding hills hoist that you just kind of screw into the ground.

That's quite industrial.

That's gonna run you some

now.

I'm making big assumptions about how robust that is.

It looks like it's metal and folds pretty reliably.

There's a big range of how good that metal could be.

I'm going to reckon that was

£60.

Hmm.

I've been looking up a lot of furniture and stuff recently.

And that's roughly around the price I would have guessed for this.

There you go.

It's one of those things where you're like, either this is quite expensive because it's good, or it's very dious.

Yeah, exactly.

They call it the Argus Lucky Dip.

I also don't know how big it is.

There's kind of a picture of a woman hanging something up.

Well, it has a total drying space of 50 meters and it holds five wash loads.

50, you can't count the individual string as like 50 meters.

They have that, yeah.

They should be saying, oh, it has a drying capacity of a square meter.

What fabric?

No, like it's a size that I Oh, understood.

Understood.

Like,

if I was like, will this fit in my backyard?

You go, well, it could fit 50 meters of line on it.

I was like, that's not useful.

And here was me hanging my washing out on one continuous linear line.

I'm going to go for 70 pounds.

Gotcha.

But for the record, and for, I was thinking 65.

Oh, okay.

Because that'd feel safer.

But for some reason, I want want to get closer.

It's very interesting.

I should have just gone for 61.

Why not?

Because I've already done this.

I've already said what I'm going to do.

Okay, fine, fine, fine.

Okay, I realize in hindsight, I should have just said 61 because there's no one else after me.

Yeah, yeah, yeah.

Okay, what do we got?

So, I have bought not this exact product, but a rotary washing line this week.

And what I found out while shopping for rotary washing lines is they're way more expensive than I thought they'd be.

This one

is £159.

£159.

Congrats.

Okay, so we have a winner.

Becca's won the first ever.

The square is right.

And

what's interesting about that is you then did stumble onto the optimal strategy, which is to just guess one dollar or one unit above the otherwise highest guess.

Because for the hairdryer, when I said 45,

you knew it was more than that.

You could have just said 46 and you're guaranteed.

There's no way I can win at that point.

Yeah, but that's less interesting for listeners.

They want to know if I'm going to get the price exactly right.

Yes.

No, you've gone for the, I want to play the game.

The strange of the game.

Yeah, yeah.

And what Calc Dave wants here is just optimal strategy.

Yeah, that's true.

And I'm going to kind of.

It's called the price is right, not the price is almost right.

The price is optimized to be right on average.

That's what I would call call it.

Someone mocked that up.

Don't do that.

I'm going to kind of ignore Calc Dave's specific question because I think it's just interesting the difference between trying to solve problems or playing a game show

for fun or the way it was kind of intended versus just the optimal strategy to win on average.

And someone called Ben Blatt went through

one and a half thousand episodes of people on the U.S.

prices right playing that guessing the price game

and worked out

how often they would have won if the last person, just looking at the last person, if the last person to guess

just had picked $1

more than up until then the maximum guess.

And it turns out if they had just done that, the last person would have won 54% of the time.

If they didn't even try and guess what the price is, they didn't think about the product at all, if they ignored any how much is this worth and just guessed $1 more than the highest bid, even though they're only one out of four contestants or however many, they would have won 54% of the time.

In reality, the last person won 35% of the time because by trying to be clever about it, they actually won less often.

Yeah.

Well, it's not being clever.

It's just trying to show off.

It's trying to show, yeah, yeah.

Well, it's trying to use your smarts.

It's trying to use your knowledge about products and prices to play the game rather than your knowledge of the game.

Following the rules.

Yeah, yep.

And so for this kind of guess the price, but don't go over strategy, as Calc Davis said, if you know it's in the zero to 100 range

and you just want to be the closest on average, if you pick the midpoint,

assuming the price is randomly between zero and 100, by picking the middle, you'll be the closest on average.

Yep.

But now you're thinking, well, what should you do if someone else, like you can't go over?

I would argue it's the same.

You still pick the midpoint because when we were playing then,

if you think the actual answer is above what the other person's guessed, you should guess $1 more.

Yep.

If you think it's below what the other person guessed, you should choose $1

because you're claiming the entire range.

Well, now you're basing basing this on where the two people are playing.

Yes.

But if four people are playing

and the first person says for $50

and you're like, I think it's less than that, you're second and you go a dollar.

Well, then...

Yeah, you know, 100%.

This is assuming,

well, for Calc Dave, we got the two-person version, 0 to 100.

If you've got multiple people, it gets much more complicated.

The price is right.

It's also much more complicated because there's no upper bound.

So there's no range that you can try and split the middle of.

Sure, yeah.

So the optimal strategy in general will depend on the range and depend on the distribution of prices within that range.

Because they probably won't be evenly distributed.

So every amount's equally likely.

Yeah.

Depending on the sorts of products, there's going to be a bit of a distribution.

In general, I don't think there's optimal strategy.

If you're playing a two-person version over a set range with equally likely amounts, you're going to be right in the middle.

Because if you're not in the middle, someone will claim the bigger range by either going one or one dollar more.

You can claim whichever is the bigger section the other person's left you.

And if you're the first person, you want to go in the middle.

What Ben Blap did was

look at all the prices rights over one and a half thousand episodes to kind of get that kind of bakes in what the range is and what's going on and show that

if you're last, the the one dollar more strategy is gonna you're gonna win more often than not yeah which is very impressive

and people don't do that well i guess because generally people know the rule is that you don't want to go over so everyone is going to guess either the price that they think it is like deep in their heart or slightly lower than the price that they think it is because they don't want to go over they're not going to over guess so you're more likely that whatever the top guess is it's not going over because no one is trying to go over you're 100 correct the stats have shown exactly what you're saying that people tend to guess down

and

what you really should do is actually go a little higher so the so if you're not last you should at least go higher than you think although if you're the top guess you're going to get sniped by the last person unless the item is 61

and that person guessed 60 so you went 61 that's pretty yeah you're right it's very unlikely to get it exact I think the game show even gives you a bonus if you get it exact because it happens so infrequently.

But I thought we could play

a different game from the prices, right?

And we'll see how we go.

So this game is called Now or Then,

and you will be shown six products that will all have a price.

And

four of them will have their current price.

Two of them will have a price from the past.

I haven't bothered getting the products, and we're going to assume that you're just going to be guessing at random.

All right.

Because you could put a lot of effort into working out if you think it's the now price or the then price, or you could just assume it's completely random and see if you can win the game or not.

And the prices are put out in a circle.

So I've written now on four cards, and I've written then on two cards, and I've put them in a circle.

You can try and guess them in any order you want.

You just need to end up with three correct guesses in a row.

It's guess now or then, and you need to end up with three touching guesses that were correct.

I'm looking at stuff and I'm struggling to understand why anyone would do this.

Okay, so.

It's a game show.

You got a lot of time to fill.

That's true.

May I please have that one?

I'm going to say now.

You think this is now?

It was now.

Okay, let's go the closest one.

down from it.

I'm going to guess that that one is...

Oh, there's more nows than there are thens.

Okay.

All right.

So I'm going to go now again.

Now again.

Yep.

Turning it over.

It's now.

Ooh.

So now there's two nows and two thens.

Yep.

Left.

You've only got to get three in a row.

Okay.

The furthest left, I'm going to go for now.

It was then.

Oh.

Okay.

And the one above it,

I'm going to go for then.

You think this is then?

It was a now.

Ooh.

This is going to be tricky.

I don't want to spoiler it, but you can definitely win this.

Oh, okay.

So why can you definitely win?

Because,

well, it's a 50-50 chance.

Yeah, there's two cards left you haven't flipped over.

One's a now, one's a then.

But what happens once you've seen one of those?

Oh, do I get to choose all of them?

Yeah.

Oh, okay.

Right.

For some reason, I thought this was my last go.

Nope.

Okay.

What's your strategy to definitely win now?

Okay, well, we know that whatever one I flip over,

if it's a,

let's say the bottom one, if I was to say that that is

now and it said then,

then I know that the last one is now and it's the top one and that links all of those.

So either you win on this next guess or that will give you the information to win on the following guess and both of those will give you a chain of three.

It doesn't matter which one.

Yeah.

So for completeness, let's do it.

Oh, okay.

All right.

Then.

Correct.

You won.

All right.

If you then have been wrong, you would have won on the next move.

Yeah.

That does not seem like a good game.

That's because if it's stripped of all context, it's not.

Right.

But of course, if it had pictures of products and prices on there, then I would be overwhelmed by all the information

and confuse myself.

And you would be trying to use your knowledge of the products and what the prices probably are and what they were in the past

to guess.

Has anyone like gamed the system?

The person Ben Blatt, who analyzed the one and a half thousand episodes, also looked at this game.

And if you do what I've done and just ignore the products, it's just now or then in that ratio, you can win every single time.

I was going to say, I feel like then there's no way that you could.

You can't.

You can guess three in a row to start with.

And depending on which ones you get right, you can do the remaining ones in the order to work out the information to fill in the final row of three.

You cannot lose that game.

However, when they analyzed the last 13 years of price's rights, the person playing that game won 68% of the time.

Because the other people just weren't looking at the obvious answer.

Correct.

They were trying to think about the prices.

Yeah, I would have been one of those people, I reckon, too.

Like, I would have easily that makes for a better game show.

Yeah.

But in reality, you should just play it using cold,

cold clinical algorithms.

Yeah, it's like that, you know, one of us always tells the truth and one of us always tells the truth.

Exactly like that.

It's exactly one of those puzzles.

You just got to think through it logically and you're guaranteed to win.

I think it's very funny that a game show has a game

where optimal strategy wins 100% of the time.

Yeah.

And the track record is 68% wins.

Yeah.

But it's weight that a TV, don't get me wrong, it wouldn't be on the show if people played it properly they would have swapped it out for a different game of course but people don't humans god we're so stupid

this has made me sad

it's just it's humans i mean i love this stuff because you know i love puzzles and games and you're easily obsessed by them

but um

we don't live our lives thinking through things logically like this.

And I'm not suggesting we should make all our decisions this way, but I just think humans, we get, we're too easily drawn in by the details and the illusion of how smart we are and thinking it through and using our insight

to be clever when in reality, just do it

logically.

I've talked about this before on the podcast, but just the amount of feed, like positive feedback I got when I had my 2020 tour booked, which obviously got cancelled.

There were all like 30 dates.

And instead of listing it chronologically, I listed it by city, by alphabetical order, because I, no one needs to know what my schedule is.

They just need to know if I'm performing near them.

Bingo.

And the amount of people like, oh, God, this is so much easier because they could see if I was performing in Birmingham or Leicester like quickly.

Yeah.

And I thought that that was a very obvious way to put dates on posters.

And it wasn't until people responded that I realized that no one else lists them that way.

Because we're so obsessed on the order in which we're doing these things.

Even the marketing teams, the managing teams, they're all thinking in terms of chronologically.

And it's like, well, but that's not the audience is that.

my tour might be in chronological order on my there you go change it to alphabetical

we're officially halfway through the fringe right now i'll check my slide i might have done 13 shows in chronological order and you've now shamed me i here's me all blah blah blah use logic yeah and then and if it's a slide even worse because it's going to take them longer to see if you're performing near them

So

the conclusion is we're all doofuses.

Yeah.

We could use a bit more logic in our life.

Yeah, that's true.

So there you are, Calc Dave.

I don't know what that answers, but you're welcome.

Yeah, I'm going to give it a ding.

Thank you for pointing out how flawed we are.

The logical step is to give it a ding.

Our next problem was sent in by Tim,

who refers to episode 111, where aspiring tooth fairy Beck mentioned that her going rate, because Beck is the adult tooth fairy, for those of you who aren't familiar with this, and she's also, she's fine, she's great.

Her going rate when she's buying teeth off other fully grown adults, there's a lower rate for broken split teeth.

At least you were theorizing you would offer less if the tooth wasn't in good condition.

Yeah.

Now, it turns out Tim has, for reasons I don't want to go into, a large plastic tooth filled with most of their own baby teeth at the back of a drawer somewhere.

They think maybe the local tooth fairy did a return to sender and got a refund from his parents.

But whatever the case, for some reason, Tim has held on to their own baby teeth.

And in the intervening years, every single one of them has split in twain directly down the middle.

So Tim's problem is, Beck, as a definitive tooth expert, is this common for teeth to do?

Or did I, this is Tim speaking, just have particularly poor quality teeth?

And they do add, maybe they didn't drink enough milk as a child.

So Tim had assumed it was maybe because the teeth had been mouthless for two decades.

Why did you have to say it like that, Tim?

Yeah, it's not a mouth that's toothless.

No, it's a tooth that's mouthless.

And maybe...

Being mouthless for so long, the teeth are dried out.

But then Tim thinks they've seen very old teeth in museums that seem to be fine.

So what's going on?

Beck, there's no one with more experience of a wide range of old teeth.

Well,

a couple decades old teeth than you.

What can you tell us?

Okay, well, firstly, let's not oversell my knowledge of teeth.

I am not medically qualified.

That's true.

I think I deliberately said experience.

Do you know what?

This is me across the board is I know a little bit more than most

on weird subjects, and it's enough to get by.

You know more than 90% of the population.

Yeah, and there's plenty.

Yeah, but not as much as actual experts.

However, I do know someone who is an expert.

What?

I know.

I went back to the source.

Ah, here we go again.

Dent to Sophie.

I feel like sometimes I'm co-hosting a podcast with Dentus Sophie.

Honestly, that would be a great spin-off.

I would love that.

I love Dentist Sophie very much.

So I sent this problem to Sophie who said,

oh, that's so interesting.

Of course.

I wonder if it's the molars, incisors, and canines all affected.

If it's just the molars, that sort of makes sense because they have multiple roots, like a milk stool.

So have a natural weakness through that vertical axis.

Right.

Like a milk stool.

Yes, I got stuck on that as well.

Have you ever heard of a milk stool?

No.

I assume dentists are just obsessed with milk.

Is that where you eat and drink nothing but milk for multiple days?

And it comes out as a milk stool.

And he's always a milk stool.

No, I'm going to send you a picture that Sophie sent me

after I asked what a milk stool is.

Oh, it's a stool.

It's just a stool.

It's a small, so I guess like a milking stool for sitting on when you're milking.

Oh, it's not because the legs look like udders.

No, no, I think it's because you'd have a little stool that you'd sit on to milk a cat.

Now, this one has three legs.

She'd point out because she just did a quick Google.

But yeah, if you imagine a molar, yeah, it looks a bit like a little stool.

Got its little roots that come down.

So dentist Sophie said, you know, maybe it's split because it's naturally divided into those segments.

She then went on to say the canines and incisors though are single-rooted and tapered, so that's very curious.

A nutritional defect is an interesting hypothesis, but I doubt that's the case.

Teeth are incredible in their embryological origin and subsequent morphology, which is a fantastic sentence.

Love it.

Now, do you want me to expand on that sentence?

I want you to unpack that sentence.

Yeah, because you say it again, very clearly.

Yep.

Teeth are incredible in their embryological origin and subsequent morphology.

So she's saying they're interesting when they first develop and they just keep getting more interesting as they grow.

Yeah.

So first of all, I didn't know that what's on the outside of our teeth and what's on the inside of our teeth are made from different things.

And that's why Sophie thought it's so fascinating that these teeth split, because then you need two different problems to create this stool.

Because you've got enamel on the outside.

Yes.

And love and happiness on the inside.

I'll tell you what's on the inside.

So when I asked Sophie to explain

all of that, the embryological origin and the morphology.

Got it.

She said, your teeth are made from ectoderm and mesoderm.

So imagine you've got a horseshoe shape of white play-doh sitting on top of an identical horseshoe shape of yellow play-doh.

Got it.

So basically we're building a door.

Oh, you think about the shape of your...

Yeah, yeah, yeah.

Along the horseshoe shape, you make 10 indentations, not enough to perforate the white layer, but enough to create a cup shape.

Inside the white play-doh are cells called ameloblasts, and they are awesome because they make enamel.

Enamel is the strongest thing in the human body, so they have a lot to brag about.

So inside that indentation, they get going on making enamel.

In the yellow play-doh below, the mesenchyme, you've got other cells called odontoblasts.

So we've got ameloblasts making enamel and odontoblasts.

Odonto means tooth.

Blasts are cells that build.

So these are tooth-building cells.

Yeah.

Anyway, they build the rest of the tooth, dentine, pulp, cementum, and pyrodontal ligament.

Each of those 10 indents you made at the start become a baby tooth.

And that's a simplified version of dental embryology.

You know what I really like?

You can tell.

when the different aspects of that were discovered by how they were named.

So the really hard to find stuff has got like, what was the name of the cells that make enamel?

Ameloblasts.

Yeah, that's a modern name.

And at the very end, what are they calling the bits once they've been made and we can see them?

Cementums.

Cementum.

Someone just went, that's hard.

Mendentine.

Cementum.

Mendentine.

Periodontal ligament.

Yeah, exactly.

Yeah.

Interesting.

Oh, by the way, the bone that holds your teeth is called the alveolar bone.

Right.

So that's like the, and the horse shoes go on to form your upper and lower bone.

Oh, and it's called the alveolar bone because all the, because of the tooth sockets, those little cup indents.

Alveolose, alveolus?

A-L-V-E-L-O-U-S means small hollow.

Oh, yeah.

And those baby teeth in those little indents start forming.

while in utero around week six.

Week six?

Week six.

Teeth time.

And I think we've mentioned it before, but you see those x-rays of um babies heads terrifying baby heads because then yeah we we end up with the adult teeth

yeah it's i love it it's great so

we've unpacked that sentence yep so the components of the crown top bit yep differ from the components of the roots bottom bit that's what we just discussed before yeah so sophie's guess is that if it was a defect of the enamel

That wouldn't necessarily translate to a defect in the rest of the tooth.

So, I mean, I have terrible enamel.

I have to use special toothpaste.

Right.

That's not too abrasive.

Because my poor enamel is like, oh no, it's too abrasive.

Yeah, exactly.

So

Sophie's saying, like, even if your enamel has defects, your whole tooth shouldn't.

Yeah, my teeth are fine.

It's got other stuff.

Yeah, exactly.

Yeah, yeah.

It's like if the paint's coming off of a bit, like,

or like if the paint's coming off something metal, you might start rusting.

It might start rusting underneath, but the falcon doesn't immediately fall out.

I would rather have the enamel.

Yeah, yeah.

Sophie's guess at first was that maybe it's just affecting the molars because of dehydration and the weakness spots and that sort of thing.

But then she was thinking more about the enamel issue because initially she was like, well, if there's an issue with the enamel, it doesn't necessarily mean it's an issue with the rest of the tooth.

However,

when your baby teeth fall out, now.

Can you think just visually, what is the difference other than size between a baby tooth and an extracted tooth?

Oh, like an extracted normal adult tooth and a baby tooth.

I didn't think there was a difference.

I mean, I think maybe because

I've seen a lot.

Yeah, this is what I'm saying.

You've got a lot of experience of looking at teeth.

Like by size, I mean, obviously, baby's teeth are smaller, but they're also smaller for another reason.

Oh.

Why is that?

They don't generally have much of a root.

Oh.

So think about when your baby teeth come out, they're kind of like

rootless at the bottom.

They don't have the whereas extracted teeth, you either get a nice big table

or the all the molar ones.

So the reason I didn't know this is that when the baby teeth fall out, they fall out because the roots have been resorbed.

Resorbed?

Yeah.

So the roots break down.

So the other teeth are like the whatever the name of the cells that make teeth were like, you know what?

We're having having that back

give us back all that root material we're making adult teeth yeah exactly so so if he says to simplify under each baby tooth is an adult tooth as the adult tooth grows towards the surface it puts pressure on the baby tooth root that pressure triggers cells called odontoclasts the odontoclasts release acids to break down the hard stuff root cementum and dentine and proteins and enzymes to break down the soft stuff like collagen.

So odontoclasts are also tooth destroyers.

This allows the baby tooth root to resorb fully until the tooth is so wobbly you can wobble it out.

Right.

So

is what dentist Sophie you're trying to say is baby teeth are inherently weakened

because they were partially eaten

before they were kicked out.

Yeah.

Exactly.

So it very possibly could have been an enamel defect because a lot of the other stuff has actually broken down

in the drawing

phase.

Yeah, yeah.

A couple of other awesome facts.

Your enamel is made from crystals.

Great.

Crystals are

hydrozyapatite.

Zyapatite.

Hydrozyapatite, I'm guessing.

And you can find that in metamorphic rocks, too.

Great.

Lovely rock.

So basically, the mesenchyme does so much work laying down the foundation of your tooth, building the ligament that holds it to your jawbones, the pulp that brings blood and nerve supply, as well as the regenerative capacity of teeth and the dentine which hydrates the tooth.

And the ectoderm covers it with spectacular crystals and calls it a day.

Oh, we get it, Sophie.

Teeth are great.

Yeah.

And then Sophie ends by saying, so all I'm really trying to say here is, can I interest you in a bespoke milk stool?

And I'm going to add that because when Sophie sent me that picture, she was like, oh, I was just thinking that might be a nice stool to get.

And then she saw the price.

so the final part of my answering this question Matt is do you want to guess the price of that milk stool I love it now you've given me the information that a dentist winced at the price yes

it's in australia it's in australian dollars okay in aussie dollars i'm just gonna go back and look at the picture again now do i have to get it right without going over

yes so here's the thing that stool if it was in ikea

would be a 30 buck stool maybe 50 bucks but now I look at it, the legs are all slightly different.

It's in they've been handmade.

That stool,

I'm going to say $300.

Higher.

No.

I'm going to give you three attempts without going over it.

Okay, a thousand bucks.

Oh, you just went over.

I went too far.

Too high, too far.

What was it?

$920.

$920.

That's nuts.

We'll stick a photo on the...

That's about $307 a leg.

But you get the top for free.

Yes.

So

I think I've answered that question.

I think so.

The answer seems to be baby teeth are

weaker than you think.

Especially once they've come out.

Yeah.

They don't have so much good stuff in there.

So it could have been an enamel issue.

It's not a diet thing.

But yeah, it could also just be the way that you've kept them and the dehydration and that.

It could just be that they've dried out in particular and had a weakness.

And that's what

maybe there was, maybe you didn't brush them after they fell in.

But it's not normal.

So congratulations, Tim.

Yeah.

Anyway, let me know, Tim.

Let us know.

Go to the problem posing page, click solution instead of problem,

and let us know if that's a ding for myself and dentist Sophie.

And if you want to sell those teeth at a discount rate, back's your guy.

Yeah, let me know.

Do they come with the box?

That's what I want to know.

And we're on to any other business, or as we will call it this episode, any other blurgness.

Bjorkness.

Bjorkness.

Why?

Not quite.

No, not the same country, but still.

And I'm excited to say that we heard from Tekler or or Tekler, we weren't sure how it was pronounced, T-H-E-K-L-A,

who made a teeth offer.

We discussed this on episode 113.

They had the messiodons, messiodons, messiodons, the single tooth that are grown between

the front teeth.

And I'd asked them to let me know what they thought was a fair price.

And they said, I reached out to you previously.

Having now heard your thoughts on a price point and having discussed it with some friends, I'd be happy to part with my lump of enamel for £20.

20 pounds oh as a bonus i can also bring it along to the edinburgh fringe to eliminate any risk of it getting lost in transit

that includes shipping yeah that's a good price but also we are halfway through the fringe so have we missed that well at the time of listening we still have a week of edinburgh fringe remaining so i either have it now yes or

in the last week Which is an organic way to say everyone, you've still got one week to come and see our shows

in Edinburgh.

What time is your show?

Would you believe it's at 6.30 6.30 in the Pleasant Scourtyard?

What about yours, Beck?

Oh, it's at 7 p.m.

at Appleton Tower.

Go in a balloon.

Is that why neither of us can watch the other person's show?

It is.

But I've had a lot of wonderful people say that they've seen your show and they love it.

It's about your show.

So we're both great.

Our next bit of AOB was sent in by Felix, who has a solution.

to Beck's Lido problem.

This is where Beck,

you didn't say it was a problem.

You just complained about outdoor British swimming pools for an extended period of time.

And you were right to do so.

Felix wants you to try Rice Lip Lido.

They say it's got a beach, it's got trees and now this might bump you over the edge.

It's got a little miniature railway.

I would go for the railway and potentially stay for the summer.

There you go.

Okay.

Well, that way, let's just maybe you emotionally commit to the miniature railway.

And when you're there, maybe the Lido will win you over.

Do you want to do a should we do a problem squared excursion to Rice at Lido before the summer runs out?

I would love to.

My mum's going to be in town in September.

Maybe I'll take my mum.

Yeah.

Sold.

We also heard from Nicole, who was also responding to something else in episode 114.

Chip to dip ratio.

Nicole said, it's funny.

I knew exactly what problem Higgins was talking about, even though I never actually struggled with it.

It is so simple.

Always ensure you have leftover dip.

Oh.

Dippables, while they can be eaten on their own, are often dry dry and boring, but leftover dips can be upcycled.

Leftover salsa goes into my weekend bolognese.

Doesn't matter if it's half a glass or just a spoonful.

Cream cheese or dairy-based dip also go into pasta sauce for me.

More saw vegetable spreads, beetroot, nepscombe, sweet potato, get recycled into salad dressings or spreads on sandwiches, which are my go-to week meal lunches.

Just because it says salsa on the tin doesn't mean it can only be eaten with nachos.

Be adventurous with your cooking.

You might discover something delicious.

I love listening to the show, and I never knew I needed a nerdy comedian until I was introduced to Matt.

And Beck is essential to keep his explanations understandable to the everyman.

You two make a good team.

Thank you for making it available to everyone.

You're welcome.

Hey, look, considering,

considering we're trying to get more people to get on board with Matt's.

Very true.

They need the everyman.

They need this guy.

They need

mummy like me who's like, break down the big words, please.

Now, and symmetrically, I get to be the everyman saying, but why do you need so many teeth?

Exactly.

Between us, between us.

We are normal.

There you go.

Great, on average.

Philip here says, hi, Beck and Matt.

Exclamation mark.

Love the show.

Insert as many blasts as necessary here.

Great.

I'm glad that meme's evolving already.

They just finished episode 115, the previous episode, and they've got some bigger letters than the Hollywood sign.

Philip, what do you got?

So they say it's nowhere near 1 billion point.

Okay.

But lots of schools and colleges in the western U.S.

put a giant letter on a nearby hill to represent their school.

That's why I don't stand around school

state.

They might put a giant letter on me.

So they say Lassen High School in California has a 580-foot-tall L.

That is a big L.

That's a lot of feet.

A lot of feet.

Western Colorado University has a 420-foot W.

That's nuts.

And if Philip has done the math right, they're saying that's like 716K point and 518K point fonts.

Oh, my goodness.

So over half a million point.

And they've provided links that we will share.

That's amazing.

I think they may be the biggest letters that we have in the running.

Well, further to that, I did let Rhys James know that we had

covered the inconsistency.

Oh, really?

This is the comedian who made the original joke that started this all.

Oh, Rhys was great about it.

Rhys

said,

love that.

That's when you know you're really cutting through.

I've had enough pedantic comments to know it's closer to about 50k-ish.

Is that correct?

People have already sent in the correct point size.

Oh, that's so great.

And then Rhys did say, look, in the Mock the Week game that they were playing that this clip was taken from, the answer is a billion, and you come up with the setup.

Oh, right.

Yep.

And Rhys was like, oh, it's the point size of the file.

So Rhys does point out, it's not like they could go, it's a bit, well, actually, I think you're fine.

It ruins the joke.

Despite the fact that Rhys has clearly had Nerdery come after him

for

the fact that it was wrong this was still very very good about

and he said I'm thrilled thanks for telling me excellent and while Rhys James thanks us we would like to thank you we would yes thank you for listening thank you for in advance for telling your friends to listen and a special thanks to all of you who are financially supporting us and making this podcast possible for everyone else and if you would like to support us you can over at patreon.com forward slash a problem squared where where you will get to listen to our bonus podcast.

I'm a wizard.

It's pretty good.

You get a little insider information we don't talk about on the main show.

Yeah.

And

you are in with a chance for having your name read out at the end of an episode when we choose three at random.

We will mispronounce it though.

And this episode, those people are

onsenge.

Will I am wall a

da

Noeli

Noonten?

Thank you so much for supporting us and thank you Matt

for remaining rigid and being easy to move from rental property to rental property.

Yes, thank you me for

the farty

and

a huge thank you to the Alan Key.

Oh, good work.

Puts it all together.

Nicely done.

Our wonderful producer, Laura Grimshaw.

And I would like to say to all of you,

faval

or

avskked or adjo.

One of those might be pronounced correctly.

And we'll mean goodbye in Swedish.

Meatballs.

Meatby.

Okay, back sure shot.

Now, if I believe correct, you ended on a hit last time.

You did.

Okay.

So I

got lucky.

Yes.

C eight.

C8,

adjacent to your previous hit

is a miss.

Ooh, okay.

And I'm going to come in with I nine.

I nine.

I nine

hit.

Yes.

The cold algorithmic logic wins again.