114 = Delectable Dips and Dealable Decks

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

But instead of raw meats and or meat substitutes, you bring us problems, and instead of cooking them, we solve them.

Unless your problem is, what do I do with all these raw meats and/or meat substitutes?

In which case, this podcast is exactly like a barbecue.

Your grill masters are Matt Parker, a mathematician and YouTuber who enjoys repurposing old code to solve new problems.

Like a cook who might fashion a spatula from an old fly swatter.

And me, Beck Hill, a comedian and writer who will often stray from the problem and fall down a rabbit hole.

Like a cook who perpetually steps away from the grill to wander aimlessly through the sight of a large, densely built Warren.

I view my code like people view leftovers.

Oh, so you're like eating people.

To reheated back up again, I'm like, ah, I can chuck in a few new bits, reheat it back up again.

And then serve it to the customers.

Yeah, exactly.

And listeners, you are those customers.

Yeah, exactly.

On this episode, I worked out what's the deal with

cards.

I see what you did that.

I thought the deal pun was so strong, I didn't bother writing the rest of the sentence.

But you really gave up on it towards the end.

Yeah, I know.

If you said, What's the deal with cards?

I could have sold it.

I could have sold it.

It's in the delivery map.

no i find out what the deal with dips is and there'll be any other barbecueness

how are you matt i'm good i'm good i'm tired yeah i can tell

you a little bit grumpy that's true i got more sass than normal i do apologize you're like a toddler that's just woken up after a nap

bit blurry-eyed you know that when when when toddlers still have the little tears in their eyes, but they've just stopped crying, so they're kind of, yeah, that's you right now.

No, I just got a lot of stuff on at the moment because you and I are both still honing our Edinburgh Festival Friend shows.

Yes.

Which we will bring up every episode until it's too late for anyone to buy any tickets.

After which, I'm on tour, standardmass.com slash shows

for all your CMAT inner show needs.

And my book came out in paperback.

Love Triangle.

Paperback came out.

Ah, so it's more affordable now.

Way more affordable.

The has plummeted.

So now it's bendable.

That's fun.

A book about angles, you can actually bend it now.

So that's

something there.

I did the Joe Marla podcast.

I'm just looking for a sense of recognition.

People are sitting there going, oh, what's happened to my podcast app?

It's just stopped.

Nope.

That was me.

That was you buffering.

Staring at Matt in silence.

You told me

what the podcast was about.

You said it's a rugby podcast.

Correct.

It was not a rugby podcast.

Joe Marla is a rugby player.

Right.

Well, he retired last year, I think.

And so he did play for England, like, played at an international level, like a very good, famous rugby player.

Obviously, that level of competitive sport, particularly something with that much, you know, getting knocked around, you've got to retire at some point.

So he's like

mid-30s.

He's like, I'm too off of this.

Retired.

Does a podcast.

Nice.

And it was fun for two reasons.

The second reason is just it was very friendly.

The fantastic PR people at Penguin were like, would you want to do the Joe Marla podcast?

I was like, yeah, why not?

I was timing up, but no idea what it was going to be like.

Lovely.

Just really good fun.

Really nice.

Him and a guy called Tom, chatting away.

Very funny folks.

Very slick, very professional.

A lot of fun to be around.

I had a great time.

Slightly, actually, you know, one of the knock-on effects of me doing a rugby podcast is I get a bunch of credit with people I don't normally get credit with.

So the pub that we often go to after recording, The Star, here in Godaming,

the people who run it are all big rugby fans.

Ah.

And I have never had more respect

from

the people who run the pub than when they found out I did the Joe Marla podcast.

Nothing else I've done has even made a tiny dent.

Well, they wouldn't have noticed.

Like one time I walked in and Mike, one of the guys, is like, was this you?

And it was the Donald Trump tariff video.

It just popped up on his YouTube feed.

Okay, yeah.

Up until then, they had no idea I was just that guy who came in with a Labrador that was very friendly.

Yeah.

He's like, What are you doing on YouTube?

I'm like, that's the thing I do.

But now, Joe Mila podcast is also broken through the noise because he played for a local, local-lish team called the Harlequins.

When we were leaving, we were just chatting, and he, when he was younger, lived not far from Godaming.

He was in this area.

And he mentioned he's like one memory he had because he was he was a kid at the time and he remembered going to a pub called the refectory it's one of our favorite local pubs and i'm like oh i know the refractory i love it he's like yeah it was always great because they had those tubes that your order would go up in like a pneumatic tube like a pneumatic tube nice and i was like

you saw the tubes because they were removed long before my time.

They were a thing of legend.

Oh, I'd heard rumors of the tubes i never fully believed they definitely existed and was true ah but doing a podcast with a rugby player played for the england team and he just casually drops into conversation confirmation that the pneumatic tubes because they used to take your order apparently behind the bar and then like thump and that's so cool pneumatic tube into the kitchen

He's like, yeah, I saw the tubes.

I was like, I know they see the tubes.

They've got one of those at the postal museum, so I got to try one.

All of the messages came from some small children on the other side of the museum.

Now, you and I are pretty good at not being starstruck by famous people.

We work with famous people.

We're very chill.

Yes.

I don't have to try that hard with sports personalities because I already don't know who they are and I'm in no way in awe.

But I appreciate it.

I think it takes a phenomenal amount of work, more work than being a comedian to be that level of sport.

Like that, the competition is phenomenal and the dedication and training and everything.

So I'm very impressed when I meet professional athletes.

So the whole time time I've been real chill.

But at the end, I just went, wow.

As we're saying goodbye, I'm like, wow, I can't believe I met someone who saw the tubes.

He thought it was the funniest thing.

We weren't recording.

It was like the funniest thing he'd ever heard.

Because I guess he's sick of like rugby people like, wow, I can't believe I meet it.

I'm like, wow, the guy who saw the tubes.

And that's who he'll always be to me now.

Yeah, weirdly, I gigged in Brighton recently and I caught up with our friend Sibley Delisle, who's a fantastic laserist.

That's all my lasers.

And he said, oh, there's this new brunch place that's just opened called The Canopy.

It's really nice.

They do really good brunch, very affordable.

So we went there.

We're sitting there chatting.

I like to sit with my back to the window.

Otherwise, I get distracted by what's happening outside.

As we're talking, the chef.

comes out and is chatting to the people behind the bar.

I'm like,

that's Chef Michael Bremner from Great British Menu.

Like some years ago as well.

I think it was during lockdown, maybe.

But I was like, oh my gosh.

And then Seb turned around and was like, oh, yeah, yeah, I think I remember them saying like it was a good chef.

And I was like,

and I kept getting so distracted.

He could see me looking over his shoulder as like Seb could see me, but I wasn't paying attention.

And I was like, I'm just going to ask for a selfie.

And he was like, okay.

So I went up and I was like,

Are you Michael?

And he was like, yes.

And I was like, can I have a selfie with you?

I saw you on Great British Menu and I think you're amazing.

And he was was like, oh, sure.

So I got a picture.

Like, I have interviewed John Cleese.

I have

interviewed

like Christina Ritchie.

I have

I regularly spend time

with quite like well-known people in my job.

Is that a selfie we could put out on the yes, we can put it on social media.

I want to see

because someone who's been on both sides of those selfies,

I want to do a little reading of the the facial expressions.

I was so happy.

I'm so, so happy.

Yeah.

And he's holding his spatula.

It's a fly spotter.

Yeah, yeah, yeah.

So how are you, Beck?

I'm good.

It's been warm, the weather.

It's been real warm.

So last week I went to a Lido.

British listeners, I have a bone to pick with you.

So the pool that I used to, I grew up going to, firstly, had like quite a little grass area around it.

you put your towel out there there's some trees yeah so you can like lie under the trees when you're not swimming

it's hot shade okay this lider and i've been to other lidos i know it's not distinct to this lido but it was a hot day right it's the first time i've been to a lido on a hot day firstly

no grass concrete oh nothing but concrete or concrete or concrete not much space

when it's hot so much concrete no shade no shade no no literally no shade nowhere to get there get that right into the the concrete.

Big high brick walls.

Yep.

Concrete.

It was like a prison.

I'm not joking.

It was like being in a prison.

Wreck time.

At the later.

It was like a prison, but worse because, and I say that loosely, I've never been to prison, so I realize that I can't.

I suspect people would disagree with you.

I would say it's worse because, at least in prison, you're not

trying to sunbathe by a soup of children.

They're all screaming and everything.

It was so busy.

It was so full.

There was no space to like properly swim or splash about or whatever.

There's nothing like that.

It's like one pool.

It's not like they've got

a big one and then a small one.

Because normally there's like one that people can splash about in and be stupid, and then there's another for laps and stuff.

I understand in Australia we have more space.

I get it.

I get it.

But there was a park next door.

There is, there's land.

To the grass walls.

Yeah, but it was, it was outside of the big, tall brick walls

because it wasn't in trouble.

You had to go over the razor wire.

Right, it was so close.

I would not be surprised if there was razor wire at the top.

It was so.

And we had to pay £12

for one hour.

£12 an hour.

A pound every five minutes.

I couldn't believe.

I was.

And I went with another Australian and she and I were like...

This is hilarious and frustrating.

I only went because it was my friend's birthday.

Oh, that's very nice of you.

But then afterwards, also for my friend's birthday, we went to see the band Sparks playing at Hammersmith Apollo.

And I was familiar with some of their songs, but seeing them live, I was like, oh, I get it now.

Oh, right.

They've been going forever.

They've got like 28 albums.

They're like, it's like you, Matt.

They're the most famous band you've never heard.

Yeah.

I would say we might have been the youngest people in the in the crowd.

Yep.

It was, but they're fantastic.

They're really good.

But the thing that I got distracted by was the stage lighting.

Oh.

Now, it was like

sort of

rods of light, maybe like a meter or so.

My meter or so.

A lot of light.

Oh, like a fluorescent tube on its own.

Yeah, yeah.

Yep, got it.

And they were sort of, it was set in almost a grid type

pattern.

Right.

So then they could make different

patterns and stuff like this.

And there was no real, like, there were patterns, but they didn't like...

represent anything in particular or whatever.

Sometimes they made it look a bit like it was raining.

Other times it was like, it was all very random.

But I felt very nervous because I kept thinking, at any point, this could accidentally make,

like, when you've got a grid and you're lighting, you could make some pretty offensive patterns.

Now, those offensive patterns pop up occasionally in maths when you're doing things with symmetry and whatnot.

And they're commonly referred to as the unfortunate fourfold rotational symmetry.

I love this.

That was what I was worried about.

And then my friends and I were talking about this and saying, and because it made me think of segmented displays.

Oh, yeah, yeah, yeah.

And how

you could create segmented displays.

They could have done numbers, letters, or something.

And that made me wonder, do you reckon that they have some sort of program that if they are sort of doing

a random pattern type thing?

Yep.

to make sure

that it never shows anything offensive or accidentally spells out like bum or something.

I've been looking into things like that because I've been putting together the lights for my show.

Ah, so the stuff I've seen there, probably you get LED strips now that you basically put inside a plastic tube with the frosting to make it look like those lights.

Yeah, and I'm sure that's what it was.

Yeah, and then you get all the you can have DMX controllers that are doing all this stuff.

Very interesting.

I haven't got the time.

I wish I could throw myself into it fully because it looks so amazing.

I haven't got time for another hobby at the moment.

But I will say, your friends of mine, Fox Dog Studios, Pete and Lloyd, they were hired many years ago by the BBC to run an interactive stall for school kids at the Big Bang Fair.

The BBF.

The BBF, the Big Bang Fair for the BBC.

And I've done stuff there as well.

I happened to be there the year they were there.

So I hung out with them for a bit and chatted about the system.

But it involved allowing thousands of teenagers loose who

as in about without significant adult supervision

free entry text boxes oh no that will then automatically appear

on screens around the game zone or whatever it was foxtograph running now it takes less than a second of thought to realize how that's going to go wrong yep because they don't want to sit there and manually check every single word so they had to come up with a system to stop that from happening so they basically had to come up with all the words

or fragments of words they wouldn't want to appear on the the screen and then run everything through the check before it goes anywhere near the screen so i imagine some people were likewise tasked with here are all the symbols

but you've got to then convert the light signal into what it's going to look like as a readable signal because just two contrasting colors could do it three contrasting colors with the right arrangements could do it.

I think it'll be an interesting challenge how you'd code up that filter, but I almost guarantee it exists.

I I suspect what is more realistic is it wasn't random and they just programmed it to do very specific patterns that weren't bad or rude.

I think that was a substantial chat.

I suppose we should answer some problems.

Podcasts get to these burgers before they burn.

Oh, problem burgers.

Our first problem comes from the problem posing page on a problemsquared.com.

This is Mark who said, take a sorted sorted deck of cards, i.e., a deck sorted from Aester King of Spades, then Aester King of Diamonds, then clubs and hearts.

Shuffle the deck in the following way.

One, hold the deck face up in your right hand.

Shall we do this at the same time as you're reading out the steps?

Yes.

I sorted a deck into the four suits.

They're all in order.

What order did they want the suits in?

They've suggested

spades, diamonds, clubs, hearts.

Okay, so what do I do now?

I'm holding the deck of cards.

They're in the order that Mark has requested.

Okay, so you're holding the deck face up in your right hand.

Face up in my right hand.

So that's like I can see the king of hearts now.

Yep.

Take the top card from the deck

and hold face up in your left hand.

Done.

Take the...

Top card from the deck in your right hand

and place it on top of the deck in your left.

Done.

Take the top card from the deck in your right hand and place it on the bottom

of the deck in your left hand.

Then repeat steps three to four until the entire deck has moved to your left hand.

So I'm taking the cards off the top of the deck on the right.

Okay, so I'm now working my way through the deck, taking cards off the top, and I'm putting them alternately on the top and the bottom of the other deck.

Oh my goodness.

This is going to take a while.

Okay, while Matt does that, I'll read the rest of the question.

Great.

Now repeat this again and again.

What?

I've not even done it once.

They said after 12 reshuffles, you will get back to the original deck order.

However, the curious pattern emerges at 9.

Oh.

The cards will now be grouped by rank rather than suit.

And those groups will be ordered like so.

1 King.

2 Queen, 3 Jack, 4, 10, 5, 9, 6, 8, 7.

Notice how the numbers climb from one end towards the other end and then at 7 reverse back through the deck into leaving.

Yeah.

Also notice that within each group, the order of the suits will be the same order as the original deck, but this also reverses when the cards go back through the deck.

I.e.

the order of ones is spades, diamonds, clubs, hearts.

Then the order of kings is hearts, clubs, diamonds, spades.

I hope you can explain both why it repeats and why you get this curious pattern.

Why?

Why?

Why, Mark?

well i what's wrong can do one half of that okay each of these shuffles which is not a great name because they're going to the same place every time but let's just call it a shuffle each of these specific shuffles because they're always identical have to repeat

at some point they have to go back to where they started yeah it's like when you do a rubik's cube you do the certain exactly yeah because there's only a finite number of arrangements a deck can be in

and so if you're doing the same thing every time, you're eventually going to come back to a state you've been in before.

I know we've discussed this for other problems.

Because either you'll do every single one of them and you finally get to the last one and you come back to the beginning.

Or more likely, you will hit the starting state and then loop back.

Or it might be that you go for a while and then you hit one that you did.

halfway through and then you go into the loop.

You've got a loop with a little tail it took to get in there.

So

any set shuffle you do, if you do it long enough, you'll get back exactly where you started.

It can just take a different amount of time.

This one takes 12 rounds.

You know at the very beginning when we started taking the cards off, we put the first card in my left hand and the next card, we started with it going on top and then went under, then on top, then on under.

If you accidentally do it the other way around, if you did under first, then on top, then repeat all the way down,

you would still get back to where you started, but it would take 51 shuffles wow so it's 12 is the one that mark mentioned the quick one that

seemingly trivial change over four times longer wow 51 and i know that because i did it using terrible python code so to answer the second question for mark it will always repeat doesn't matter what shuffle you do if you do it consistently or any consistent series of shuffles as long as you repeat that series over and over again you'll come back to where you started so if the number of cards in a suit is 13 yeah but it ends up being one less than that.

The number of cards in a pack is 52, but it's one less than that.

Yeah.

Is there another move we can do to test to see if it's one less than that?

What would that test be?

I have no idea.

That was for you to answer.

I'm not a mathematician.

We're looking at number of cards, numbers in a suit.

The only other thing you have there, really, is the number of suits, which is four.

Yeah.

So it needs to be something that takes three.

Yeah, I think it'd be reverse engineering.

It would be very difficult.

Unless it was a really contrived shuffle.

Yeah.

That just like moves the middle to the top to the bottom and back.

Did I

proved it?

I'm done.

Yeah.

So I put together some code and I just wrote a little algorithm which takes the deck as just a list, 52 values in a long list.

And then takes them out of one list and puts them into another list according to the algorithm.

So it takes them all off the bottom because you're dealing from the face and then alternately adds them to the beginning or the end of the other list until they're all done.

So coding wise, it was pretty straightforward.

Then I had to set up different decks, put it in, see what comes out, and then feed it back in again and tell it to stop when it hits something it has seen before.

So that's how I got it to,

it can tell me how many it takes before it goes all the way through.

Now I was just kind of doing that to make sure my code was working and I understood and I got the 12 that Mark mentioned.

I not only have that it ends up back where it started started, and it's that interesting one nine in, but I've got every other single state it goes through along the way.

So I thought I'd show you that, and we'll have a little look and see if there are any other fun patterns.

Yeah.

We can verify what Mark said, that that definitely is the thing that happens part way through.

Would you like to see the output?

I can do this either way.

It can either be all the cards numbered 1 to 52.

Or it can be the face values.

It'll be like ace 1, 2, 3, 4, 10, jack, queen king.

Face values.

Face values, it is.

Okay.

To see a whole deck at once, you've got to make the type quite small.

Oh, I don't like it.

So.

Well, tough.

It's like looking at a magic eye.

It's not look like looking at a magic eye.

I wonder if it's a sailboat.

Yeah, exactly.

Dolph.

Okay, so.

We'll put these in the show notes.

But there's your 12 states.

And the first one is just ace, two, three, four, then up to king.

And then it repeats ace all the way up.

The lead card is interesting.

The top card in the deck goes ace, two, four, eight, so it's doubling.

But then it goes three

and then doubles to six, and then two, and then ten, and then seven, then king, king, king, right at the end.

I don't like that.

No, it's not pretty.

That's not a nice pattern.

When I was scanning through the in-between states, there's no other ones that really stood out to me as being like, oh, that's interesting.

Other than because that's all of it for me.

Oh, really?

Well, here's the one that Mark got excited about.

And you see, this one here starts.

It goes King, King, King, and then Ace, Ace, Ace, and then Queen, Queen, Queen, 2, 2, 2.

So this is the one that Mark was talking about.

9 in, where they're all

in batches of four.

Yeah.

After that, they're in pairs.

It goes King, King, Ace, Ace, Queen, Queen.

And then all the pairs repeat.

And then you have another one that looks like mess.

And then the last one is right back where it started.

So I stared at that much like you and thought I can't see anything particularly interesting in that.

I then had a look at the one I did where you start under instead of on top, which takes 51,

and the ninth one in totally different.

I was like, Well, hang on, it's both the ninth one in

and it's the third one from the end.

So, I went and looked at the third one from the end of the other system, and it's the same.

Ah, it's the same setup.

I was like, that's curious.

And then I tried it with smaller suits, so I took out all the kings, ran the simulation again.

It takes a different number of times to repeat.

So if we get rid of all the kings from the deck and then run the code again, it now takes 24 deals before you're back where you started.

But one,

two, three before the end, yeah, queen, queen, queen, ace, ace, ace, jack, jack, jack.

You need to have an even number of suits for it to work.

So if you just took out all the spades, wouldn't work.

Right.

If you took out the spades and the diamonds, it would work again.

And if you take cards out of a suit, it still works.

Okay.

So now I'm just, I use the code so I could rapidly try a bunch of variations because if something breaks it, then that must be important.

Or it persists despite a change.

That's giving us an insight into where the pattern's coming from.

And so what we've learned is it's not the ninth one in that's special.

It's the third one from the end.

It has to be an even number of suits.

Doesn't matter how many cards are in a suit.

So there are constraints now on when it works.

So for me, this is like the beginning of the problem solving process.

Here's a pattern and it's something like if it's algorithmic or involves a situation, I'm like, well, what happens if I take or remove things from the situation?

And that tells me what's important.

So the key for me was realizing, oh, it's not how far from the beginning, it's how far from the end.

And I was like, okay, yeah, because if the deck has to end up

back the way it started

you could think of a shuffle which is the exact reverse, where you start with a deck, and then you take the bottom one off, then the top one, then the bottom, and the top, then the bottom, the top, and you're putting them into a new pile in order, which is just the exact reverse.

And if you do that three times, that's what goes from

having

them in the perfect order to this interesting order.

And that's the actual journey that matters because that's the one that's the same every time.

And so then I wrote out a simplified version of

a deck of cards, four suits,

and each suit only got four cards in it.

So I've numbered the cards one to four, and then one to four, one to four, one to four.

And then I reversed the pattern back, and it works.

Yeah.

And so

the reason it works is

partly what we spotted before, and partly something I didn't really notice about the second last one.

So I actually reversed it from the middle out.

So I did the cards in the same order.

So I took the middle one out and put it back on the bottom.

And then the one that would have been above that back on the next one from the bottom.

And then reversed all the way back.

And you're kind of going from the middle of the deck and then bouncing backwards and forwards as you go out, which is reversing when you started in the middle and you were adding backwards and forwards on both sides.

And it means you're going forward through some suits and backwards through other suits.

Right.

Because the ones where you're going like further into the deck are in order, but the ones where you're going back in the deck from the middle, you're going backwards.

And the only ones that line up

are the

extreme ones.

So your fours

all end up being paired together because they're the same distance away from the middle.

All the other ones are in different orders apart from the middle one.

Because once you're halfway in from one end, it's the same as being halfway in from the other.

You reach the same card.

And so you end up pairing up the extreme values and the middle values.

And the other ones, you flip half of them, and the next time you do it, they get paired up.

And so then you've actually got a whole bunch of pairs,

and then those pairs get paired up, and that becomes the four groups of four afterwards.

That was a very hand-wavy explanation.

Yep.

I've convinced myself why it works.

Okay.

And it's because you're starting in the middle and you're going in different directions.

There's no really neat

reason other than it happens to happen because of the way the cards are.

There's not like some beautiful explanation behind it.

It's not some sort of Fibonacci.

No, you know, it's not like, yeah, oh, it turns out because the golden ratio.

Or sometimes it's really pleasing where you're like, oh, it's the explanation of this because if you think of the deck upside down, it's a triangle.

Like, those things I love.

It's not one of them.

Right.

It's just, it's what happens and will always happen if there's an even number of suits.

You You know what?

I'd really like to do what would you really like to do?

Attach a different colored piece of wool.

Yep.

To each card.

Yep.

Long, long bit of wool.

Yeah, baby.

I hear what you're saying.

Yep.

And then do this technique.

And see what braid you end up with.

Yeah.

You would see the pattern.

That would make it a lot more visual.

A friend of mine, Henry Segerman, who's a mathematician who juggles, Henry and I got bored one time when he was staying over.

And so we got some juggling balls and tied ribbons to them.

Great.

And so as you're juggling, you braid the ribbons like a three-ball cascade.

And then we realized one of us could do a three-ball cascade and one of us could do the opposite of that facing each other.

And the balls are tied in pairs.

And so as you're both juggling, they never get tangled.

Cute.

And then we looked up braid identities.

So we could be doing different juggling patterns, but still the ribbons would never get tangled.

And we had some good nerdy fun.

I should make a video out of that.

Yeah, that would be really interesting.

It'd be really good fun.

I would be really interested to see you pair that with a hairstylist.

Right.

Because you can get really intricate hair braids

done.

I mean, braid theory is a whole area of maths.

So I imagine braid theorists have talked to hair braid people

and compared notes.

But I'd always heard that a juggling a cascade is equivalent to a braid.

And we wanted to do it with ribbons.

But you're right.

It is, because when you're braiding, because I used, when I had long hair yeah i used to braid my hair the normal braid the most common ones the outside in yep so that's if you were juggling you'd be sort of throwing inwards throwing inwards and then the reverse is the normal juggle where you're throwing up in the middle you're throwing in the middle yeah and that's when you're braiding outwards and that's the one that gets you the french braid the one that's sort of on top that i think is prettier but anyway i'm biased so you're right this shuffle feels a lot like that

You could maybe do it with a reduced deck like I did on paper and see it.

That would probably be one of my next steps

if I felt like there was something else interesting in here would be to draw that diagram, like have arrows.

This goes here, this goes there.

Yeah.

And see if any patterns come out.

But the wool idea is even better.

I also want to point out that this was not the problem you were going to solve originally.

No, not when we met this morning.

Yeah, you needed an item which

we went on a hunt for and quickly.

We went out for lunch and it wasn't in Sainsbury's where it was meant to be.

So I was like, I'll do it next time.

So you knocked this together in quite a fast yeah i don't know if that reflects on me in a good light or a bad light i think i think it's very impressive but i also think it should be mentioned in case anyone points out glaring errors oh yeah

that's more like it that's yes yes yeah there's any and waviness i did this over lunch so

go easy and i know that there's going to be hundreds of you listening going, but I sent it a problem.

Why would you choose that one?

Because I I was looking for one I could do over lunch.

I looked around the room.

You know, you got to make up a fake name.

You literally dropped a bunch of like cards of cards this morning.

So I think that was fresh in your mind.

You weren't browning me, weren't you?

I was, yeah, that's right.

I was planting all the problems.

Yeah, it was me.

I sent you this one.

I was getting out the podcasting kit this morning.

I knocked some cards off a shelf.

I was like, oh, I've got cards.

I was like, how do I trick Matt into making me a friendship bracelet?

The long game.

Anyway, In conclusion, it is because it is, it's not, it's neat, it's a fun pattern.

I don't think it's a particularly nice reason why it appears.

It's kind of fun, I guess.

The big thing is, Mark saw something interesting, thought, huh, and then investigated it.

And we had a play, and it was a lot of fun.

And it doesn't always go anywhere.

And this time, it just turns out it is.

And I convinced myself it's true.

They can't all be bangers.

The end.

our next problem is from Higgins who went to the problem posing page at a problem squared.com and they open by saying beck and matt very polite I have a problem good

I mean I'm sorry to hear that but also good yeah that's what why why we're here yeah I thoroughly enjoy bringing in snacks for my teammates at work that's not the problem they specify that

imagine imagine if it was the problem That was the problem.

Yeah.

And they enjoy it much too much.

Often, this is in the form of a dippable thing.

And the dippable is dipped into.

While I bring the food in for my teammates, I also partake of the food items.

And this is where the problem starts.

For example, if I bring in tortilla chips and salsa, I will likely end up with leftover chips or

the exclusive or leftover salsa.

I will then go refill the dippable or the dip so as to use up my leftovers.

And most of the time, I create the inverse situation and repeat the cycle until I get lucky enough to correctly estimate the right amount of dip and dippable

needed to have no leftovers.

It is important to note that I do not like wasting food.

Well, that much is very obvious at this point, Higgins.

How can I solve this problem and avoid eating the bulk of the food I bring in for my teammates?

Love the show.

Blah, blah, blah.

Okay, Higgins, you want me back?

Thank you for the help.

Can we name this, by the way, this, this, because I feel like this is a highly relatable problem.

I think we've all been in the situation where we've ended up with leftover dip or leftover dippable.

Yeah, some kind of food that requires the other.

Yeah.

And if they're not eaten in the correct ratio, you've got a useless portion of one.

Yeah.

Thus creating...

Is it the Higgins problem or the Higgins

paradox?

Yeah, and I guess what Higgins is trying to say here is they bring in a reasonable amount of chips and dips.

A few chips and dips are consumed by their colleagues and themselves until the limiting reactant runs out.

From what I'm reading between the many lines,

Higgins then goes home and goes like, oh, I better get more chips because I've only got dip.

It's like, oh, no, I've only got chips, better get some dip.

And they eat multiple times the original

office food before they've depleted and eventually they've come into phase.

Now, I'm going to argue that my favorite part about,

because I love going to a picnic, love a barbecue, love a, you know, bring some stuff along.

Theme of the episode.

My favorite part about it is

leftover

dip or dippables.

Gotcha.

Because then I'm like, oh cool.

I can go get the thing that it needs and then I've got something to eat as I go that is half the price.

Okay.

You're halfway there.

I'm halfway there already, right?

The meal's meeting you in the middle.

And I feel like that's kind of the plus side of this scenario.

Yeah, but Higgins is a finisher completer.

So am I.

But then it is half price until you buy too much of what's missing.

And then you've got to buy the original one again.

At this point, you've just paid for the whole meal.

But then you've got to buy the other one again.

And then you end up paying two or three times

before they come into phase.

What you don't want is the amount, the unit purchase of dip and dippable to be close but not quite.

It's going to take longer, take longer to come back into phase, just like if two frequencies are slightly off, the beats are super long.

Yeah,

whereas if you just like the dips

was

twice the dippable,

boom, you got it in one extra purchase.

Yeah, yeah now I can't help but feel that this is a trick.

Oh, by I think it's very smart.

Okay, this is my theory.

Well, no theory.

This is a hypothesis.

Okay, yeah, because I haven't tested it yet.

My hypothesis is the brands or whatever, because often they'll create, they'll put out both the

chips and the salsa.

Yeah, yeah, yeah.

And they make it so that it's not the right amount.

Yep.

So that you're forced to keep purchasing.

Love it.

It's like how uh

i think we've talked about tim tams yeah hot dog same thing they're like quite often you'll end up with an uneven like magnum ice creams now come in packs of three three

who does that masochus never have a prime number of things

in a food packet that's designed to be shared yeah

the only time that that would work is right now there are three of us in the room you've either got the prime number of people or one very hungry person they're the only solutions to that problem yeah now in the case of the three ice creams both would work.

Yeah.

But in bigger situations, no.

Yeah.

So.

In that case, you're blaming Big Dip.

Blaming Big Dip and Big Dippable.

Yeah.

They're like the constellations.

Yeah.

Yeah.

So I've made this my dinglet because

that's a short problem for that's a short problem for new listeners, yeah.

Because I think it really matters.

There's so many variables.

So many.

So for me to do this as like a proper big main problem, I would have to go back to you, Higgins, and be like, right, how many teammates do you have?

Is it the same amount of teammates each time?

It's the viscosity of the dip.

Yeah.

I'm going to guess that Higgins likes to switch it up because otherwise you're going to be known as tortilla and salsa.

No, you don't.

You don't want to be tortilla and salsa person.

No.

You want to be snacks person.

I'm going to guess that that's the case.

And I'm also going to guess that occasionally someone might stay home.

There also might be people with specific

food.

Somebody who's like, I can't have Tatsuki.

I can't have it because I can't spell it.

Is that the rule in your house?

You can't eat it unless you can spell it.

I can barely have guacamole.

Still, not every time.

That's all French cuisine out there.

You haven't had a croissant for years.

No, I dream of a croissant.

But get.

But

I'm here eating things like ham,

soup.

Oh, we've reached silly o'clock again.

Thank you.

I'm going to do a quick test.

We couldn't get what you needed from Sainsbury's.

No, but we could get what I needed.

So you've gone for some brand name tortilla chips, not the faux ritos, which is.

Oh, who do we call them?

Yeah, I came up with that name when I was doing Questing Time in Manchester.

I'm sticking with it.

Great.

I feel like there's a crossover from people people who went to Questing Time and who listened to this.

So I imagine it's big.

About two people just got very excited.

So I'm going to open them up.

So this is my very specific scientific theory.

What I wanted to do originally was to weigh the chips and the dip and then weigh them

after we've eaten to see what was left.

But we don't have weights.

So I'm just going to get us all to maybe unobserved

that by all I'm including producer Laura.

We're going to dip a whole tortilla chip into the dip.

But then I think on the counter three, we'll compare our chips to see if we tend to go for the same amount of dip each.

Okay.

So because we don't have scales, what I think I'm going to do is count how many tortilla chips

in this packet.

Love it.

And then I'm going to see, first of all, we'll do the blind thing to see how much we load onto a chip.

Yep.

Just out of interest.

Then we can kind of guess.

Blind dip.

Yep.

Like how many it might take.

Then we will work our way through this salsa, the three of us.

Right.

We will work out how many.

Then we're going to work out how many tortilla chips we get through.

Because we've got a significant amount of tortilla chips in this pack.

Yeah, and a lot of dip.

Yeah.

We'll count how many tortilla chips it takes us.

And then we will see how

count how many are left.

Right.

Okay, fair enough.

All right.

So everybody take a tortilla chip and dip it without looking and then hold just to start with.

Oh, my goodness.

Okay.

And then, and then we will.

You go first.

I'll close my eyes.

All right.

Okay.

This is so ridiculous.

Okay.

I'm holding it under the table.

I'm going in.

Producer Laura.

Okay, everyone.

What do we got?

I've gone for quite a lot.

I'm a big dip guy.

You are the big dipper.

Laura goes for very little dip, I've noticed.

This is interesting, but I think it's good.

This is why I couldn't just test test it on my own.

I love the fact that we could just hang out as humans, but no, we're having a simulated hypothetical party right now.

Technically, it worked.

You've brought these in for your colleagues, too.

So, this is very realistic.

Just call me Beck Higgins.

Beck Higgins.

I'm going to keep track of how many I've eaten, by the way.

Are we allowed to take these down the pub until we finish them?

If we keep counting, of course, we'll keep counting.

This is number seven.

So, because we don't have time to casually wait to see how long we get through these no

uh we'll continue to do this because we're finisher completers we are gonna finish either the dip or the chips yep and then we'll record a voice note once we have a solution yep great once we have a result oh did our post recording drinks just get tax deductible heck yeah they did all right

So the result of that will appear here.

Okay, here it is.

Now,

Thanks, Studio Matt.

It's on location Matt here in the pub and we have just finished snacking.

Yes, here is on location back

to say that we got through 82% of the dippable chips in the pack because we were left with an amount that were far too small to dip.

We got through 82% of the pack before we ran out of dip, which was 86 chips that we counted.

Yes.

Out of 105 for anyone who's curious.

The dip itself is 300 grams of salsa.

So we worked out that each chip carried 3.5 grams of salsa.

That might be interesting to know should you have shop-bought tortilla sized chips that you're working with.

And in terms of conspiracy theories involving big dip,

80 to 20 ratio is about as far as I would push it

to make people have to buy more.

Like that's right on the cusp of

recurring purchases for as long as possible.

Yeah, because we were looking at the packet going,

I probably wouldn't buy a whole new salsa for that.

It was close.

But it was, yeah, it was very close.

It was very close.

And to be fair, we went for a hot salsa, which meant that we probably didn't eat through it as fast as people would have if it was a mild salsa.

I think the 80-20 ratio stands.

Back to you, studio, Matt, and Beck.

Well, we'll let those guys get back to the pub, shall we?

Yes, yes.

Now, my solution for you, Higgins.

My solution to the Higgins paradox is that you should do a similar experiment

and then just make your own salsa make your own dip oh work out oh i love it how much it takes you to get through a packet of tortilla chips or make your own tortilla chips i love making tortilla chips is that do you do it with pitter bread no flour oh you make it properly well when i do burritos i like to do my own tortillas anyway

and again i never make the right amount so then i just hang them out in the oven

to to get real crispy crispy.

Cut them up into little triangles with a little bit of olive oil, a bit of salt, wing them back in the oven.

Ooh.

Ooh.

That's a tasty.

They're really good.

All right.

Well, do you know what?

Let's stick some links to some tortilla chip and dip recipes.

I would just encourage everyone to go for less pre-packaged stuff.

The exact amount you want.

That's my advice.

Good advice.

Yeah, thanks.

Take down Big Dip from the inside.

And for any other BBQ B-ness.

Wow.

Matt, you've got a plug?

I do.

I'd like to promote Beck's Edinburgh Show.

It's called...

Oh, hang on.

Guess who's Beck?

Back again.

Beck Hill's back.

Tell your friends.

Beck Hill's back.

Beck Hill's Beck.

Yeah.

Tell your friends.

Yeah.

Great.

I've seen a lot of places get it wrong because clearly they've decided to type it out instead of copy-paste.

They copy and paste.

Yeah.

Shout out to listener Sonny who did the photos.

Oh, and listener Sonny.

Yep.

And then the lovely William Andrews who put it into a nice poster.

But yeah, check out my Instagram, Beckhill Comedian, if you want to see my Edinburgh Fringe poster.

Or indeed, if you're in Edinburgh, you might get, I'm going to do limited edition of flyers again this year.

Oh, interesting.

Yeah.

Hand numbered.

I'm doing all flyers different as well.

But I'm doing it using Turbo Python code.

Yes.

I'm very excited about this.

Yeah.

Each flyer has 102 different symbols on it.

Or not all different.

Any two flies will have one and only one symbol in common.

So it's a

Edinburgh-wide game of double.

The printers are not happy with this game.

No.

And I think

they can play with the posters too.

Yeah.

Happy about that.

It's great.

Yeah.

But it happened.

I love that.

See you all there.

Links to the shows in in the show notes.

Eve got in touch on the problem posing page.

Not the first time they've used it because they're the one who posed the problem where they had chopped karate chopped a board in half.

Like a total badass, their words, but they are correct.

And this is way back in episode 106.

They wanted some ideas on what to do with their karate chopped board to commemorate the achievement.

We had a couple ideas.

They've picked one

and they've sent us a link to it on their Instagram.

So I'm just going to open that and have a look at what they did.

Oh, that's great.

Okay, Beck, I'm going to hand over to you to describe what we're looking at here.

Yeah, because I suggested they maybe, because you get so much

art,

I'm using that term loosely, where it's like engraved.

or burnt into it with a with a fun phrase.

Quirky expression.

You don't have to be crazy to work here, but it helps.

Exactly.

That kind of thing.

And then I suggested a bunch of very dumb

affirmations.

Yeah.

And Eve has chosen one of them.

It's a really good one.

Which is, it's fiber chop somewhere.

It's five of the chop.

Somewhere.

Eve has posted it saying it's definitely not perfect, but I'm really pleased with how this turned out.

Eve, you should be.

It looks fantastic.

I wouldn't change a thing.

It was great to use my wood burning tool a bit more.

Whoa, there you go.

Look at that.

Even if my lettering is a bit wobbly.

Eve, I think your lettering is your lettering is better than my handwriting.

It's now hanging above the desk in my spare room/slash office, office, for those work from home days.

I am absolutely thrilled.

Good work, Eve.

This makes me very happy.

It is indeed 5-0 chop somewhere.

Eve's shown how

they put the board back together again with paint and glue and a bit of, do a bit of sanding.

Little guide.

I missed the guide.

Build the finish.

And there's also a picture of Eve chopping the block.

No.

Oh, look at that.

In the first place.

place mid chop so this is great that's very good we'll pop this link in the yeah show notes as you did tag us as well very impressive we've also heard from Keith great name who's listening through episode 111

and Beck mentioned she's a very visual thinker yes that sounds like you and they've commented on Beck thinking about how a lot of people evoke mental images

they just wanted to give a shout out to all the sufferers of Aphantasia, like Keith, who are unable to create a mental image.

And they've given us the Wikipedia entry to Aphantasia, which we will put in the show notes.

They discovered a couple of years ago

that they and other people can't literally see pictures in their mind's eye.

They always assumed that when people talked about a mental image, it was a turn of phrase and not literally an image.

in your head.

So thanks, Keith.

Shout out to everyone who doesn't have mental images like that.

It's very interesting because Keith explains a bit more about it and how once they realized this was something that they were doing differently to how other people are imagining things, it made sense why people would complain about seeing a film of a book they'd read and say they didn't enjoy it because the film looked different to how they imagined the book.

And they've just realized, oh, that's why, because other people when they read books have mental images of what's happening.

And Keith doesn't.

That's great.

Yeah, they also said that it's why they've never really been into reading books, which makes sense.

Yeah, it makes sense.

But have been interested in photography

because it's the creating of the images and helping recall things.

Yeah, yeah.

Keith also goes on to say, I think I'm at a disadvantage when trying to recall things, particularly when trying to describe detail like a person or a location.

It's not that I don't know what they look like or can't describe them, but it's more of a feeling and list of descriptors than a photo.

Do you have any advice on improving memory and recall for non-visual people?

I don't because it's not something that I have, so I have not had to.

But I'd be interested to know if any of our other listeners have aphantasia and what they've done.

If you've got any advice for Keith on ways to help memorize things.

I'd be curious to know, because a common way of like memory trick is to use a journey you do frequently.

Yes.

We're very good at remembering those.

It'd be curious to know if you've got a Fantasia

how you recall a journey.

And depending on

that done.

Yeah, because I used to do one, which was the walk from my house to this office.

Because I can picture several key points along the way and they're surprisingly little discrete locations.

But depends how if you think about a journey, a walk that you do frequently,

what that's like, maybe there's an equivalent way to then attach concepts to each of however you've split that up in your your memory already yeah yeah well we also found out after that episode that producer laura grimshaw has synesthesia so laura has certain colors

that are evoked by words and sounds and letters

yeah aren't we all different yeah it's great i love this it's very cool keith also says thanks for all your hard work on the excellent podcast thanks keith no blas and as we near the end of the podcast all that's left is for us to thank, obviously, all of you.

We really appreciate all of you.

But we also specifically want to thank our lovely Patreon supporters who go to patreon.com forward slash a problem squared.

They also get access to our bonus podcast.

Bonus podcast.

I'm a wizard.

Wow.

And early episodes.

Early episodes.

Yeah.

And there's I'm a wizard.

Is that like the kind of real like raw experience of us at the beginning of a recording session before we're

warmed up?

Oh, if you think this is slick,

you're like, ah,

polished.

Yeah, I want to know what these guys are.

What's it like to be their friends?

That's surprisingly accurate.

Yeah.

Hop on over to patreon.com.

So we are going to randomly choose three of those supporters to thank by mispronouncing their names.

And on this episode, those supporters are

ya, why, son?

Ha

are

Shabarge.

R.

Wow.

Joe Shu.

Array!

Buy Omarine.

Do-do-do-do-do.

Buy armourine.

Do-do-do-do.

Buy-amourine.

Do-do-do-do-do-do.

And finally, thank you, Matt.

Oh, thanks, Beck.

For helping me

at the grill.

You're too kind.

Flipping these burgers.

Sous chef.

They're all very well done.

Yeah.

We like a lot of the podcasts, overcooked it.

Yes, but nobody's getting food poisoning.

No, no, no.

You'll be chewing on it for a while, and you probably all reckon you could have cooked it better, and you might be right.

But it got cooked, and that's what matters.

So thank you for helping me, Matt.

I've been Beck Hill.

And as always, we want to thank our wonderful producer and editor, Laura Grimshaw, who is

like the

main host of the barbecue, I will say.

Laura sends out the invites,

yeah.

Yeah, make sure that all the dips have been topped up as well as the dippables.

Grimshaw, Grim Coleshaw.

Nah,

leave the word jokes to me.

I'm demonstrating exactly why that's our policy.

Laura Grillshaw.

Bye.

Big Q.

I didn't sink your battleship, did I, last time?

You did not.

It's unsinkable.

Or

is it?

Yep, pretty sure.

I'm going to choose

C.

No, can you imagine?

I'm going to choose

F.

Yep.

Eight.

Oh, no.

Fate.

I swore it was unsinkable, but fate

has sunk my battleship.

Well done.

I'm catching up.

Now, I'm almost 100% certain

that I've got all the ships in the cluster you had.

But

just in case I've made a mistake in my logic, I'm going to fire just a celebratory shot at H5.

H5

miss.

Okay, okay, I'm okay with that.