July 11, 2025 • 29 mins
Who created math problems? Why does one plus one equal 2 and not 11? Why do numbers go on forever? Why are numbers for counting? Why do you need math?
If you love math, this is the episode for you. And if you hate math…this is the episode for you! We’re answering all kinds of questions and demystifying the science and beauty of the discipline of mathematics with Dr. Melania Alvarez, outreach coordinator for the Department of Mathematics at the University of British Columbia in Canada. She’s also education coordinator for the Pacific Institute for the Mathematical Sciences. And she loves all your mathematical questions!
Stay tuned for a math puzzle you can solve during the episode!
Download our learning guides: PDF | Google Slide | Transcript
Math Question: There's a farmer who sells live chickens. He goes to three markets to sell them.
At the first market, he sells half of his chickens, plus half a chicken.
Then he goes to the second market, where he sells half of his remaining chickens, plus half a chicken.
At the third market, he sells half of all his remaining chickens, plus half a chicken. And he is left with no chickens.
How many chickens did he have at the start?
(HINT: No chickens were harmed at any of the markets, and they were all fully alive when they were sold.)
(Answer: 7 chickens)
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Jane (00:19):
This is But Why
Public. I'm Jane Lindholm. Onthis show, we take questions
from curious kids just like you,and we find answers. I had a
math teacher for a parent, sofor as long as I can remember,
Math has been a part of my life.My stepdad made me and my
brother do math games on longcar rides, and he still gives us
(00:44):
math riddles whenever we govisit him now, even though we're
adults. He wishes us a happy PiDay every March 14, and
suggested we use the Fibonaccisequence for our essential
passcode numbers. Don't knowwhat the Fibonacci sequence is?
You will by the end of thisepisode. Math and numbers are
fascinating, but I also know itcan sometimes get difficult to
(01:06):
wrap your head around big mathconcepts in school or on long
car rides with a math-lovingadult. So today, we're going to
demystify math. You've sent us alot of mathematical questions,
and our guest today loves all ofthem. Dr. Melania Alvarez is the
Outreach Coordinator for theDepartment of Mathematics at the
(01:27):
University of British Columbiain Canada, and she's the
Education Coordinator for thePacific Institute for the
Mathematical Sciences.
Dr. Melania Alvarez (01:35):
So my job is to go all around, showing
people how wonderful andinteresting and exciting
mathematics really is. If youinvite me to your school, I go
to your school and bring someinteresting games and puzzles
and things like that to showyou, you know, how much fun you
can have doing mathematics.
Jane (01:54):
Can you give me a puzzle?
Dr. Melania Alvarez (01:57):
Oh, there are many, but one, one that I
have. So there's a farmer, andhe sells chickens. So he goes to
the market, and in the he'sgoing to go to three markets.
And so there goes to the firstmarket, and he sells half of his
chickens plus half a chicken,okay?
Jane (02:16):
Okay
Dr. Melania Alvarez (02:16):
And then he goes to the second market and he
sells half of his chickens plushalf of a chicken. And then he
goes to the third market andsells half of the chickens that
are left, plus half a chicken.And that's it. And then he has
zero chickens, right? That's it.After that.
Jane (02:32):
He sold all of his chickens.
Dr. Melania Alvarez (02:34):
He sold all of his chickens, so yeah, no
chickens left. So how manychickens did he have? When he
sold the chickens, they were allalive.
Jane (02:44):
I don't know.
Dr. Melania Alvarez (02:48):
He sold all live chickens,
Jane (02:50):
All of his chickens,
Dr. Melania Alvarez (02:51):
All the chickens were alive. Yes, half a
chicken cannot be alive, right?So how many chickens did he
originally have?
Jane (02:58):
I see, okay, I feel like I need to write it down on paper,
though. So while, while I'mworking on this, let me ask you
some of the questions that kidshave sent us about math,
starting with some kids who wantto understand, who created math?
Sophie (03:12):
Hi, my name is Sophie, and I'm eight years old, and
live in Arlington, Virginia. Whoinvented math?
Oonas (03:18):
My name is Oonas, and I'm six and a half years old, and I
live in Brooklyn, New York. Whoinvented math?
Dr. Melania Alvarez (03:27):
Math is something that grew through
thousands of years. It's like amagical tree that was planted by
many, many people, by theChinese, the Mayans, you know,
so ancient people needed to,needed to count, at some point,
when populations started to growand we started to have cities,
we people needed to count. Weneeded, people looked at how
(03:48):
much property they had. Thereare some cultures where they
only have one, two and many. Butyou know, the more you have, you
need to, you know, to count. Youneed to measure. You need to
trade. So we started inventingnumbers. Humans started to
invent numbers and systems andsymbols and rules and but here
is the twist. So we started toinvent that. But at the same
(04:09):
time, math is not just invented,it's also discovered. There are
also things there that are thereand we and we discover, like a
triangle has three sides. Wedidn't, you know, invented that.
You know, it's that's somethingthat is true. So there are
things that we created in orderto make sense of a lot of
things, and with that invention,we also discover a lot of
(04:29):
things. So who invented math iswe humans started to observe,
started to look for patterns outof need, and we created systems
that allowed us to describe whatwe were seeing, and that's what
math is.
Jane (04:45):
So Leilei wants to know who created math problems, and
if we needed to know how to domath as humans, especially as
you say, as we started to havecommunities and use money or
barter for things. But maybeLeilei is asking, morelike, who
created the study of math, orthis idea that we teach people
math and do math problems, notjust learn how to count, because
(05:09):
we have to know how to count.
Dr. Melania Alvarez (05:12):
Well, what happened is that the moment we
are faced with a situation like,okay, I need to get to school,
but first I need to havebreakfast, I need to wake up, I
need to brush my teeth. So thenyou start thinking, okay, how
much time I'm going to take forbreakfast, and how much time do
I need to get from here toschool? So natural events that
happen to us, and these areproblems that we solve in order
(05:35):
to be able to deal with somerealities in life. So who
created problems? Well, yes,sometimes you have your teacher
creating tons of problems sothat you suffer through them and
stuff like that. But mathproblems come from the world.
When we start to wonder, youknow, the Egyptians, it's like,
Okay, how do I build thispyramid so that it doesn't fall
(05:56):
down, or it doesn't crumble, ora bridge as well, an engineer,
I'm going to build this bridge.How do I build this bridge so
that it will resist trucks goingon top? Or how, if this young
girl likes chocolate and she hasto divide it equally with
siblings, how do I divide it ina way that is fair for
everybody, you know? Or Istrategize perhaps. How do I do
(06:18):
it so that I can get morechocolate than others. So this
is where math, where really mathproblems come from. Now that
sometimes we create ridiculousproblems, like my mother bought
300 watermelons and dividedbetween me and my siblings.
Well, those are weird problemsthat sometimes I made for
school. But real math problemsreally come from the world.
Jane (06:43):
Leilei also wonders, why does one plus one equal two and
not 11?
Dr. Melania Alvarez (06:51):
We have this system of writing numbers
that is called place value. Soit depends where the number is.
So one one means that the one toyour right, the first one, is a
one, but the next one is not theone. It's a 10, you see. So for
example, the number 245 (07:09):
in that number, the two is a 200, the
four is a 40, and the five isfive. So it depends where you
position the numbers that itchanges. So one plus one is two
and one one does not representtwo, that one represents a 10
(07:30):
and then a one, so 10 plus oneis 11.
Jane (07:33):
Yeah, it's just interesting to think about.
We've created these systems thatare supposed to make it easier
for us and easier for us to dothese kinds of problems with
other people, so that your brainand my brain can match up, and
we both understand what one plusone equals. I think I see where
Leilei is coming from in that itcan be really interesting. It
(07:54):
can kind of blow your mind whenyou start to think about like,
oh, we had to make this work forall of our brains.
Dr. Melania Alvarez (08:00):
For everybody, exactly.
Kai (08:02):
My name is Kai. I live in California, and I'm four years
old. Why is there so manynumbers in math?
Dr. Melania Alvarez (08:12):
Oh, what happened is, as I said, when
counting started, we had veryfew numbers. You know, it was 1,
2, 3, many, and then somebody,instead of having three sheep,
now tomorrow, they have foursheep or five sheep, and then
they have to add that. So weneeded a system that the more we
have, the more needed to beaccounted for. And we have a
(08:33):
very, very nice system where,you know, we just basically can
go on forever and ever and everand ever and ever.
Jane (08:39):
Well, some of the kids want to know why.
Lily (08:40):
My name is Lily. I'm nine years old, and I live in
Portland, Oregon. Why don'tnumbers end?
Isla (08:48):
Hi, I'm Isla. I live in Clearwater, and why do numbers
numbers stop?
Nicholas (08:54):
My name is Nicholas. I'm five years old. I live in
Washington, DC. Why do numbersgo off forever and ever.
Jane (09:02):
Why don't numbers end? Why do we never stop adding numbers?
Is there really infinitynumbers?
Dr. Melania Alvarez (09:08):
Yes, yes. You can give me a number and I
can add one to that number, thennow you have more numbers. You
know, for example, there's thegoogol which has a one and 100
zeros afterwards, right?
Jane (09:21):
That's right before we all knew what the internet was,
googol was just a number. That'sgoogol spelled G, O, O, G O L.
Google, the internet searchengine is G, O, O, G, L, E.
Googol, the number, as Melaniasaid, is a one followed by 100
(09:42):
zeros.
Dr. Melania Alvarez (09:43):
It's a huge number. And then there's the
Googolplex, which is even largerthan that. And you say, so
there's a Googolplex, and I canadd one to that, and it's bigger
than the Googolplex. And then Ican add one to that one. And I
can keep going on and on, adding1, 1, 1, 1, 1, and 1. And I just
go on, you see. But alsoinfinity can be kind of also
(10:06):
small. Like, for example, I havea mile to go, okay? And so then
I can go half a mile, and then Igo half of half of the mile, and
then I get half and half andhalf of that, and that, do I
ever get there? No, never. And Ican go infinitely, going and the
steps are smaller and smallerand smaller. Eventually, in real
(10:27):
life we get there, butmathematically, we just can be
stuck there, trying to getthere. But if you always do
half, half, half, half, half, wewill not get there. This is what
is amazing about mathematics, isthat you can go on with your
imagination, and math is a greatcompanion for that.
Jane (10:44):
Yeah.
Dr. Melania Alvarez (10:44):
And it shows you ways that you never
thought that were possible. Andthat's what is so wonderful
about it.
Jane (10:51):
It can kind of make your brain hurt when you try to
think, think, you know, all theway out on those things, but
hurt in a good way. I mean, it'sjust cool.
Dr. Melania Alvarez (10:59):
So it is true. You talk about the hurt
and about the struggle and allof that, but what happens when
you are able to solve a problemthat is really, really hard? How
do you feel about that?
Jane (11:11):
Really good. Proud of myself.
Dr. Melania Alvarez (11:12):
Really good.
Jane (11:13):
Yeah. Like, I figured it out.
Dr. Melania Alvarez (11:15):
You get this big high, isn't it? You get
like, wow, I'm really smart. I'mat the top of the world. You
know, that's what wemathematicians live for. Do you
know we were working, westruggle, and then when you
finally solve it, and not justsolving it, is the beauty
sometimes of those solutionsthat are just like, how can this
be so perfect? And that's why.And there are mathematicians
(11:37):
that spend a year, two years,eight years, you know, 10 years,
trying to solve a problem, butthey think that it's worth it.
So that's another thing. Youdon't need to be fast to be a
good mathematician. Many kidsthink that they have to be
really fast problem solvers tobe really good mathematicians.
That's not true. You know, youcan take your time.
Tryphon (11:59):
Hi, my name is Tryphon. I'm nine years old, and I live
in Winnipeg, Manitoba, Canada.Why do people hate math so much?
Jane (12:09):
Why do people hate math so much? And we should say,
certainly not everybody, butmath has a reputation, and
people sometimes seem to feelcomfortable saying, Oh, I'm not
good at math, or I hate math, inways that you wouldn't say about
other things.
Dr. Melania Alvarez (12:24):
That's right. First of all, many times,
is the way that math ispresented to us. It's just like
a series of rules, and you're tosolve this problem, and that's
it. And that's not math,actually. That's just something
that we call practice. Real mathis not that you need to know the
tools. You need to know how toadd and subtract and all of
that, yes, but it's like youneed a hammer and you need nails
(12:47):
to build a house. So that's whatthat is. But math is thinking.
Math is strategizing. So math isnot just the solution. It's the
way to get there and how andyour thinking to get there. So
it's, so many times is how mathis... if it is just rote
learning and just memorizing allthe time, which we have to do
sometimes. But if that's theonly thing that we learn and the
(13:08):
only thing that we do, then isreally boring. I'm telling you,
if that was math, there wouldn'tbe professional mathematicians,
because no, come on, we're notthat boring people. We really
like, we're explorers. That'swhat it is, math is about
exploration. It's aboutquestioning. It's about doing
all that. If you start todislike math, and this is also
something that happens, isperhaps along the way, and I
(13:31):
find that many people say I likemathematics, but at some point I
start disliking it, because Igot lost. So what I tell kids is
this (13:40):
if you are in class and you understand that everything
and all of a sudden you don'tunderstand something, go and ask
your teacher, but soon. Don'twait a month or two months
afterwards, go immediately andask your teacher, Hey, I didn't
get this. Could you explain itto me again? Because math builds
on top. You know, it's somethingthat you it's a structure where
(14:01):
you... So if you miss the firstfloor, then the rest of the
floors are going to be allwobbly and you're not going to
understand. So don't beembarrassed about asking, and if
you're embarrassed in front ofthe class, then ask after class.
But don't leave something thatyou don't understand and say,
well later on, I'll catch up.No, no, no, no. So don't get
lost. Go for help as soon aspossible.
Jane (14:23):
That's always good practice. If you don't
understand something, ask aquestion, get some help. Math is
complicated, and if oneexplanation of a math concept
isn't working for you and yourbrain, you can always say, Could
you describe it to me adifferent way? Or maybe you need
someone to write it out for you,or help you work backwards from
(14:43):
the answer back to the originalquestion. You can ask for
different kinds of help to makesure you understand the math
you're working on in school orat home.
Coming up, why are the numbersin the order they are, and is
there really math in everything?And of course, I still have to
solve that puzzle Melania gaveme about the chicken farmer.
(15:06):
Stay with us.
This is But Why (15:08):
A Podcast for Curious Kids. I'm Jane Lindholm.
Today, we're talking aboutnumbers and math with
mathematician Melania Alvarez.We're going to solve that puzzle
about the chicken farmer in justa little while. But first, some
of your questions about hownumbers are ordered and how they
help us count.
Kai (15:26):
I'm Kai, and I'm six years old, and I live in Saint Paul,
Minnesota. Why is the numbers inorder? Why are they in 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, why can'tthey just be like in different
orders?
Dr. Melania Alvarez (15:41):
Well, so numbers are like a step ladder.
We make one number, and then wego to the next, and when we go
to the next, and then we go tothe next. So, so that's why it
keeps an order, and that orderhelps us to count. If the
numbers were all over the place,imagine we have here one, and
then comes 25 and they call 36and how can we count like that?
(16:04):
We can't! So it is like aladder. We go step by step by
step, and we gave them numbersthose names, right? Because we
need them to track things. Weneed them to trade. We need them
for things in real life. And ifwe didn't have that order, we
wouldn't be able to do that.We'll be lost in confusion in
the jungle of numbers. So, sothat's why there's a rule, why
(16:28):
we have an order. You know, it'slike why don't you build a house
upside down? Because then itwouldn't make sense. So that's
exactly the same thing withthis.
Miles (16:37):
I'm Miles and I'm five years old. I live in Quebec,
Canada. Why are numbers forcounting?
Dr. Melania Alvarez (16:45):
Why are numbers for counting? Well, the
numbers are counting because,actually, that's where math
began. Math began with counting,long, long, long, long time ago,
over 20,000 years ago. So thisis something that helped people
to survive.
Jane (16:59):
And you can think about, let's say, you had to get
through a winter, and you're,you needed to have enough crops
for your whole family to getthrough the winter. Well, you
have to know how many people arethere that I'm trying to feed.
So let's say there are fourpeople in my family. How much do
we eat every day? How many daysdo we need to get through to get
through the winter before we cangrow more food. So you need to
(17:22):
be able to count and add andmultiply to know how much food
you need to store for thewinter, which will take you to
how much you need to grow in thesummer, which will take you back
to how much you need to plantand how many plants you think
the animals are going to eatbefore you get to have them. So
how much more do you actuallyneed to plant to be able to have
(17:43):
enough to harvest... and, uh oh,there's a new baby in the
family. Now you have to do that,but for five people, so you have
to be able to do that math inorder to survive, and even if
we're not thinking about growingall of our own food now, as
families, we have to figure outhow to budget, how much money we
need, how much money we need ifwe also want to go on vacation
(18:05):
to the beach at some point. Somath is really important, and we
do like it because it helps usget the things that we want and
need, even if we think, or somepeople think they don't like
math in school.
Dr. Melania Alvarez (18:18):
You're absolutely right.
Jane (18:20):
Zoe lives in California and is seven and wonders, why do
you need to do math? We alreadysaid math has helped people
survive, but what are some ofthe other ways math is needed?
Dr. Melania Alvarez (18:30):
Well, you need to do math for for so many
things. You need to do math togo to the supermarket. You need
to do math to trade with people.You need to do math, to build a
house, to build a pyramid, tostudy chemistry, to read graphs
about how, who's going to winthe presidential election. So we
(18:52):
also need to know, like, forexample, if you are in class and
you want to go to recess and youwant to know how many minutes
are there to recess? So you cancount them. Oh, it's almost
almost five minutes to recess, Iwant to go there. Also, if you,
if you like, to trade cards. Howmany cards should I trade for
this card? That card is worththree of these cards. And now,
(19:12):
for example, all thistechnology, the phones, the TVs,
everything, all of that wascreated thanks to math.
Saanvi (19:21):
My name is Saanvi. I'm 10 years old, and I live in
Bothell, Washington. Is theremath in everything?
Dr. Melania Alvarez (19:27):
Math is not just in everything. Math is also
a way to see everything. We cansee it in patterns from nature,
flowers. There's a sequencecalled the Fibonacci sequence
that goes one one, and then whatis one plus one, is two. And
then one plus two is three. Andthen if I add two and three, so
(19:48):
I take the last two numbers andadd them up, and then I get the
next sequence. And what'sinteresting is that that
sequence represents a lot ofthings that happen in nature,
the petals in flowers, theyusually, they are Fibonacci
number. So the really math islike this invisible thread that
(20:09):
connects everything around you,and it is the spiral in the
shell. We have the rhythm inmusic, when you bounce a
basketball, too. The trees inthe branches. But the secret
about this is you can see thisif you are curious. You have to
be curious, okay, to see it. Somath doesn't necessarily scream
(20:30):
for attention. It whispers toyou, says, hey, hey, come check
it out. Well, you have to becurious. You can notice a lot
more if you're curious, and youcan have a great time if you're curious.
Jane (20:44):
Well, you came to the right place, because anybody
who's listening to this podcastis a curious kid. It's in the
name of our show. So all of thekids who are listening, that's
something that we all have incommon all around the world. We
are curious kids who want toknow more about the world. So if
you have us convinced. Let'swrap up with Alistar's question.
Alistar (21:05):
Hi, my name's Alistar. How do you become a
mathematician?
Jane (21:10):
How do you become a mathematician? We all want to do
it now, Melania, how do webecome mathematicians?
Dr. Melania Alvarez (21:15):
So first of all, we are all mathematicians.
You know babies, theyimmediately can recognize
patterns. When we are playingand we're putting cubes on top
of each other and trying tomeasure if it's going to fall or
not fall, you know, and how tobuild things when we're little,
we are all mathematicians, allof us. When we like to say, How
(21:36):
many cookies I need to bake foreverybody in my family, I look
at cool pattern, I say, Oh, howdoes that grow? How can I
continue this pattern, all ofthat. Now, mathematicians, a
real mathematician, not justanswer the questions, they also
ask questions. A mathematicianis always asking questions about
how things work, and then triesto answer it. So this is what it
(21:59):
is. Everybody, you know,everybody can do math, and we
all can be mathematicians. Now,if what you want... asking is,
how I become a professionalmathematician, usually, most
mathematicians, I mean, thereare some who don't, but most of
them go to university, andthey... they have become
undergraduates in math or a mathrelated thing, and then they go
(22:21):
for a PhD in mathematics, andthey solve problems. Now there
are two types of mathematicians,mainly. The applied
mathematician and the puremathematician. So I am an
applied mathematician and myhusband is a pure mathematician.
So an applied mathematicianpeople come with problems to me,
like I have worked with problemsin anthropology. I have worked
(22:43):
with problems in engineering. Soengineers come with a problem
and they want, you know, theywant someone who does all the
calculations and who creates amodel of what they're seeing. So
I do that. So people comes withtheir problems, and I take care
of their math problems, onlytheir math problems. So that's
right. The pure mathematicians,they ask questions if some
(23:06):
really abstract thing can workor not work, you know, and then
they start, they start workingon the on this abstract
mathematics that it looks likethey are useless, that who
cares, doing this math, thatthere doesn't seem to be real
did he originally have?
application. And lo and behold,10 years from now, 200 years
from now, 3000 years from now,all of the sudden we find the
(23:28):
application. Isn't it.. it'slike magic, and that's what is
so exciting about math.
Jane (24:21):
So I want anybody who's listening now who wants to solve
it to pause the episode and seeif you can figure it out.
Can we go through the answer andhow one way that we might be
(24:42):
able to solve it, because I wasthinking about it while you were
talking, and I think I have ananswer.
Dr. Melania Alvarez (24:47):
Okay, why don't you tell me what you're
thinking about?
Jane (24:50):
Okay, I think he had seven chickens at the start.
Dr. Melania Alvarez (24:54):
And how did you solve that?
Jane (24:55):
When you said all the chickens were alive and at the
end he had no chickens, it mademe realize that when he at the
very end at the last market, hesold half of his chickens plus
half a chicken, he would have tohave one chicken to sell,
because no chickens were harmed.
Dr. Melania Alvarez (25:15):
Yes.
Jane (25:16):
So then I sort of went from the very end to the
beginning by sort of adding andmultiplying rather than
subtracting and dividing. And soI think he had one chicken at
the beginning,
Dr. Melania Alvarez (25:29):
Yes.
Jane (25:30):
Three chickens in the middle and seven chickens at the
start.
Dr. Melania Alvarez (25:34):
And you got it absolutely correct.
Jane (25:36):
Wow, phew.
Dr. Melania Alvarez (25:37):
And that's actually, that's the way,
working backwards, you see. Soyou work backwards. You said,
Okay, I think that the first oneis one, and then the next one
will be three, because I willbe, calculating what's half, you
know, double of that, and thenyou calculate what will be sold,
and then that. So you gotabsolutely right. So in the
first market, he has sevenchickens, and half of those
(25:57):
chickens is three and a halfplus half a chicken is four
chickens. So seven minus four isthree. So we're left with three
chickens. He goes to the secondmarket, half of those three
chickens is one and a halfchickens. And then plus half a
chicken, that's two chickens.Three minus two is one. So we're
(26:18):
left with one chicken. And thelast market is one chicken, and
then it's half of a chicken ishalf, and then the other half is
one. And there we are, and oh,there were no chickens hurt in
this puzzle.
Jane (26:33):
I was so, as you said, I was so pleased when I realized,
oh, I can figure this out andget to the answer.
Dr. Melania Alvarez (26:40):
So there are many ways that you can solve
a math problem. You can you canguess, and you can do a
systematic guess, not justrandom numbers, but little by
little, guesses that will giveyou some information. So you go
on. You can start backwards. Youcan draw a diagram, too.
Sometimes you can draw apicture, and that will help you.
There are many ways, and that'swhat mathematicians use. They
(27:01):
have the different ways ofapproaching and see what work,
what will work, and sometimes itworks, and if it doesn't work,
then you start again. And that'sall there is.
Jane (27:09):
Let's end this episode there. Did you figure out the
answer to the puzzle? I willadmit it took me a while, and I
had to write myself some notes,and I did start to get really
worried at one point that Iwasn't going to get the answer
right. And then my mind startedto go blank, and then I thought
of all of you listening, and Ithought, oh no, you'll all be so
disappointed in me, or think I'mnot very smart. But as Melania
(27:34):
was talking, I realized twothings. The first was that I
just needed to take a deepbreath and start working
backwards, and I could probablyfigure it out. And number two,
that if I couldn't figure itout, that's okay. No one is
supposed to just automaticallyknow all the answers to things.
And when we're learning math,part of what we're doing is
(27:55):
learning how to solve problems.So I knew I could ask Melania
for help if I got stuck, and shewould steer me to the right
strategy. Thanks to Dr. MelaniaAlvarez of the University of
British Columbia and the PacificInstitute for the Mathematical
Sciences for answering all ofour math questions today. We're
going to add some math puzzlesand resources in the show notes
(28:18):
if you want more. As always, ifyou have a question about
anything, have an adult recordyou asking it on a smartphone
using an app like voice memos,then have your adult email the
file to questions@butwykids.orgBut Why is produced by Melody
Bodette, Sarah Baik and me, JaneLindholm at Vermont Public and
distributed by PRX. Our videoproducer is Joey Palumbo, and
(28:42):
our theme music is by LukeReynolds. If you like our show,
please have your adults help yougive us a thumbs up or a review
on whatever podcast platform youuse, we'll be back in two weeks
with an all new episode. Untilthen, stay curious.
This is But Why
Public. I'm Jane Lindholm. Onthis show, we take questions
from curious kids just like you,and we find answers. I had a
math teacher for a parent, sofor as long as I can remember,
Math has been a part of my life.My stepdad made me and my
brother do math games on longcar rides, and he still gives us
(00:44):
math riddles whenever we govisit him now, even though we're
adults. He wishes us a happy PiDay every March 14, and
suggested we use the Fibonaccisequence for our essential
passcode numbers. Don't knowwhat the Fibonacci sequence is?
You will by the end of thisepisode. Math and numbers are
fascinating, but I also know itcan sometimes get difficult to
(01:06):
wrap your head around big mathconcepts in school or on long
car rides with a math-lovingadult. So today, we're going to
demystify math. You've sent us alot of mathematical questions,
and our guest today loves all ofthem. Dr. Melania Alvarez is the
Outreach Coordinator for theDepartment of Mathematics at the
(01:27):
University of British Columbiain Canada, and she's the
Education Coordinator for thePacific Institute for the
Mathematical Sciences.
Dr. Melania Alvarez (01:35):
So my job is to go all around, showing
people how wonderful andinteresting and exciting
mathematics really is. If youinvite me to your school, I go
to your school and bring someinteresting games and puzzles
and things like that to showyou, you know, how much fun you
can have doing mathematics.
Jane (01:54):
Can you give me a puzzle?
Dr. Melania Alvarez (01:57):
Oh, there are many, but one, one that I
have. So there's a farmer, andhe sells chickens. So he goes to
the market, and in the he'sgoing to go to three markets.
And so there goes to the firstmarket, and he sells half of his
chickens plus half a chicken,okay?
Jane (02:16):
Okay
Dr. Melania Alvarez (02:16):
And then he goes to the second market and he
sells half of his chickens plushalf of a chicken. And then he
goes to the third market andsells half of the chickens that
are left, plus half a chicken.And that's it. And then he has
zero chickens, right? That's it.After that.
Jane (02:32):
He sold all of his chickens.
Dr. Melania Alvarez (02:34):
He sold all of his chickens, so yeah, no
chickens left. So how manychickens did he have? When he
sold the chickens, they were allalive.
Jane (02:44):
I don't know.
Dr. Melania Alvarez (02:48):
He sold all live chickens,
Jane (02:50):
All of his chickens,
Dr. Melania Alvarez (02:51):
All the chickens were alive. Yes, half a
chicken cannot be alive, right?So how many chickens did he
originally have?
Jane (02:58):
I see, okay, I feel like I need to write it down on paper,
though. So while, while I'mworking on this, let me ask you
some of the questions that kidshave sent us about math,
starting with some kids who wantto understand, who created math?
Sophie (03:12):
Hi, my name is Sophie, and I'm eight years old, and
live in Arlington, Virginia. Whoinvented math?
Oonas (03:18):
My name is Oonas, and I'm six and a half years old, and I
live in Brooklyn, New York. Whoinvented math?
Dr. Melania Alvarez (03:27):
Math is something that grew through
thousands of years. It's like amagical tree that was planted by
many, many people, by theChinese, the Mayans, you know,
so ancient people needed to,needed to count, at some point,
when populations started to growand we started to have cities,
we people needed to count. Weneeded, people looked at how
(03:48):
much property they had. Thereare some cultures where they
only have one, two and many. Butyou know, the more you have, you
need to, you know, to count. Youneed to measure. You need to
trade. So we started inventingnumbers. Humans started to
invent numbers and systems andsymbols and rules and but here
is the twist. So we started toinvent that. But at the same
(04:09):
time, math is not just invented,it's also discovered. There are
also things there that are thereand we and we discover, like a
triangle has three sides. Wedidn't, you know, invented that.
You know, it's that's somethingthat is true. So there are
things that we created in orderto make sense of a lot of
things, and with that invention,we also discover a lot of
(04:29):
things. So who invented math iswe humans started to observe,
started to look for patterns outof need, and we created systems
that allowed us to describe whatwe were seeing, and that's what
math is.
Jane (04:45):
So Leilei wants to know who created math problems, and
if we needed to know how to domath as humans, especially as
you say, as we started to havecommunities and use money or
barter for things. But maybeLeilei is asking, morelike, who
created the study of math, orthis idea that we teach people
math and do math problems, notjust learn how to count, because
(05:09):
we have to know how to count.
Dr. Melania Alvarez (05:12):
Well, what happened is that the moment we
are faced with a situation like,okay, I need to get to school,
but first I need to havebreakfast, I need to wake up, I
need to brush my teeth. So thenyou start thinking, okay, how
much time I'm going to take forbreakfast, and how much time do
I need to get from here toschool? So natural events that
happen to us, and these areproblems that we solve in order
(05:35):
to be able to deal with somerealities in life. So who
created problems? Well, yes,sometimes you have your teacher
creating tons of problems sothat you suffer through them and
stuff like that. But mathproblems come from the world.
When we start to wonder, youknow, the Egyptians, it's like,
Okay, how do I build thispyramid so that it doesn't fall
(05:56):
down, or it doesn't crumble, ora bridge as well, an engineer,
I'm going to build this bridge.How do I build this bridge so
that it will resist trucks goingon top? Or how, if this young
girl likes chocolate and she hasto divide it equally with
siblings, how do I divide it ina way that is fair for
everybody, you know? Or Istrategize perhaps. How do I do
(06:18):
it so that I can get morechocolate than others. So this
is where math, where really mathproblems come from. Now that
sometimes we create ridiculousproblems, like my mother bought
300 watermelons and dividedbetween me and my siblings.
Well, those are weird problemsthat sometimes I made for
school. But real math problemsreally come from the world.
Jane (06:43):
Leilei also wonders, why does one plus one equal two and
not 11?
Dr. Melania Alvarez (06:51):
We have this system of writing numbers
that is called place value. Soit depends where the number is.
So one one means that the one toyour right, the first one, is a
one, but the next one is not theone. It's a 10, you see. So for
example, the number 245 (07:09):
in that number, the two is a 200, the
four is a 40, and the five isfive. So it depends where you
position the numbers that itchanges. So one plus one is two
and one one does not representtwo, that one represents a 10
(07:30):
and then a one, so 10 plus oneis 11.
Jane (07:33):
Yeah, it's just interesting to think about.
We've created these systems thatare supposed to make it easier
for us and easier for us to dothese kinds of problems with
other people, so that your brainand my brain can match up, and
we both understand what one plusone equals. I think I see where
Leilei is coming from in that itcan be really interesting. It
(07:54):
can kind of blow your mind whenyou start to think about like,
oh, we had to make this work forall of our brains.
Dr. Melania Alvarez (08:00):
For everybody, exactly.
Kai (08:02):
My name is Kai. I live in California, and I'm four years
old. Why is there so manynumbers in math?
Dr. Melania Alvarez (08:12):
Oh, what happened is, as I said, when
counting started, we had veryfew numbers. You know, it was 1,
2, 3, many, and then somebody,instead of having three sheep,
now tomorrow, they have foursheep or five sheep, and then
they have to add that. So weneeded a system that the more we
have, the more needed to beaccounted for. And we have a
(08:33):
very, very nice system where,you know, we just basically can
go on forever and ever and everand ever and ever.
Jane (08:39):
Well, some of the kids want to know why.
Lily (08:40):
My name is Lily. I'm nine years old, and I live in
Portland, Oregon. Why don'tnumbers end?
Isla (08:48):
Hi, I'm Isla. I live in Clearwater, and why do numbers
numbers stop?
Nicholas (08:54):
My name is Nicholas. I'm five years old. I live in
Washington, DC. Why do numbersgo off forever and ever.
Jane (09:02):
Why don't numbers end? Why do we never stop adding numbers?
Is there really infinitynumbers?
Dr. Melania Alvarez (09:08):
Yes, yes. You can give me a number and I
can add one to that number, thennow you have more numbers. You
know, for example, there's thegoogol which has a one and 100
zeros afterwards, right?
Jane (09:21):
That's right before we all knew what the internet was,
googol was just a number. That'sgoogol spelled G, O, O, G O L.
Google, the internet searchengine is G, O, O, G, L, E.
Googol, the number, as Melaniasaid, is a one followed by 100
(09:42):
zeros.
Dr. Melania Alvarez (09:43):
It's a huge number. And then there's the
Googolplex, which is even largerthan that. And you say, so
there's a Googolplex, and I canadd one to that, and it's bigger
than the Googolplex. And then Ican add one to that one. And I
can keep going on and on, adding1, 1, 1, 1, 1, and 1. And I just
go on, you see. But alsoinfinity can be kind of also
(10:06):
small. Like, for example, I havea mile to go, okay? And so then
I can go half a mile, and then Igo half of half of the mile, and
then I get half and half andhalf of that, and that, do I
ever get there? No, never. And Ican go infinitely, going and the
steps are smaller and smallerand smaller. Eventually, in real
(10:27):
life we get there, butmathematically, we just can be
stuck there, trying to getthere. But if you always do
half, half, half, half, half, wewill not get there. This is what
is amazing about mathematics, isthat you can go on with your
imagination, and math is a greatcompanion for that.
Jane (10:44):
Yeah.
Dr. Melania Alvarez (10:44):
And it shows you ways that you never
thought that were possible. Andthat's what is so wonderful
about it.
Jane (10:51):
It can kind of make your brain hurt when you try to
think, think, you know, all theway out on those things, but
hurt in a good way. I mean, it'sjust cool.
Dr. Melania Alvarez (10:59):
So it is true. You talk about the hurt
and about the struggle and allof that, but what happens when
you are able to solve a problemthat is really, really hard? How
do you feel about that?
Jane (11:11):
Really good. Proud of myself.
Dr. Melania Alvarez (11:12):
Really good.
Jane (11:13):
Yeah. Like, I figured it out.
Dr. Melania Alvarez (11:15):
You get this big high, isn't it? You get
like, wow, I'm really smart. I'mat the top of the world. You
know, that's what wemathematicians live for. Do you
know we were working, westruggle, and then when you
finally solve it, and not justsolving it, is the beauty
sometimes of those solutionsthat are just like, how can this
be so perfect? And that's why.And there are mathematicians
(11:37):
that spend a year, two years,eight years, you know, 10 years,
trying to solve a problem, butthey think that it's worth it.
So that's another thing. Youdon't need to be fast to be a
good mathematician. Many kidsthink that they have to be
really fast problem solvers tobe really good mathematicians.
That's not true. You know, youcan take your time.
Tryphon (11:59):
Hi, my name is Tryphon. I'm nine years old, and I live
in Winnipeg, Manitoba, Canada.Why do people hate math so much?
Jane (12:09):
Why do people hate math so much? And we should say,
certainly not everybody, butmath has a reputation, and
people sometimes seem to feelcomfortable saying, Oh, I'm not
good at math, or I hate math, inways that you wouldn't say about
other things.
Dr. Melania Alvarez (12:24):
That's right. First of all, many times,
is the way that math ispresented to us. It's just like
a series of rules, and you're tosolve this problem, and that's
it. And that's not math,actually. That's just something
that we call practice. Real mathis not that you need to know the
tools. You need to know how toadd and subtract and all of
that, yes, but it's like youneed a hammer and you need nails
(12:47):
to build a house. So that's whatthat is. But math is thinking.
Math is strategizing. So math isnot just the solution. It's the
way to get there and how andyour thinking to get there. So
it's, so many times is how mathis... if it is just rote
learning and just memorizing allthe time, which we have to do
sometimes. But if that's theonly thing that we learn and the
(13:08):
only thing that we do, then isreally boring. I'm telling you,
if that was math, there wouldn'tbe professional mathematicians,
because no, come on, we're notthat boring people. We really
like, we're explorers. That'swhat it is, math is about
exploration. It's aboutquestioning. It's about doing
all that. If you start todislike math, and this is also
something that happens, isperhaps along the way, and I
(13:31):
find that many people say I likemathematics, but at some point I
start disliking it, because Igot lost. So what I tell kids is
this (13:40):
if you are in class and you understand that everything
and all of a sudden you don'tunderstand something, go and ask
your teacher, but soon. Don'twait a month or two months
afterwards, go immediately andask your teacher, Hey, I didn't
get this. Could you explain itto me again? Because math builds
on top. You know, it's somethingthat you it's a structure where
(14:01):
you... So if you miss the firstfloor, then the rest of the
floors are going to be allwobbly and you're not going to
understand. So don't beembarrassed about asking, and if
you're embarrassed in front ofthe class, then ask after class.
But don't leave something thatyou don't understand and say,
well later on, I'll catch up.No, no, no, no. So don't get
lost. Go for help as soon aspossible.
Jane (14:23):
That's always good practice. If you don't
understand something, ask aquestion, get some help. Math is
complicated, and if oneexplanation of a math concept
isn't working for you and yourbrain, you can always say, Could
you describe it to me adifferent way? Or maybe you need
someone to write it out for you,or help you work backwards from
(14:43):
the answer back to the originalquestion. You can ask for
different kinds of help to makesure you understand the math
you're working on in school orat home.
Coming up, why are the numbersin the order they are, and is
there really math in everything?And of course, I still have to
solve that puzzle Melania gaveme about the chicken farmer.
(15:06):
Stay with us.
This is But Why (15:08):
A Podcast for Curious Kids. I'm Jane Lindholm.
Today, we're talking aboutnumbers and math with
mathematician Melania Alvarez.We're going to solve that puzzle
about the chicken farmer in justa little while. But first, some
of your questions about hownumbers are ordered and how they
help us count.
Kai (15:26):
I'm Kai, and I'm six years old, and I live in Saint Paul,
Minnesota. Why is the numbers inorder? Why are they in 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, why can'tthey just be like in different
orders?
Dr. Melania Alvarez (15:41):
Well, so numbers are like a step ladder.
We make one number, and then wego to the next, and when we go
to the next, and then we go tothe next. So, so that's why it
keeps an order, and that orderhelps us to count. If the
numbers were all over the place,imagine we have here one, and
then comes 25 and they call 36and how can we count like that?
(16:04):
We can't! So it is like aladder. We go step by step by
step, and we gave them numbersthose names, right? Because we
need them to track things. Weneed them to trade. We need them
for things in real life. And ifwe didn't have that order, we
wouldn't be able to do that.We'll be lost in confusion in
the jungle of numbers. So, sothat's why there's a rule, why
(16:28):
we have an order. You know, it'slike why don't you build a house
upside down? Because then itwouldn't make sense. So that's
exactly the same thing withthis.
Miles (16:37):
I'm Miles and I'm five years old. I live in Quebec,
Canada. Why are numbers forcounting?
Dr. Melania Alvarez (16:45):
Why are numbers for counting? Well, the
numbers are counting because,actually, that's where math
began. Math began with counting,long, long, long, long time ago,
over 20,000 years ago. So thisis something that helped people
to survive.
Jane (16:59):
And you can think about, let's say, you had to get
through a winter, and you're,you needed to have enough crops
for your whole family to getthrough the winter. Well, you
have to know how many people arethere that I'm trying to feed.
So let's say there are fourpeople in my family. How much do
we eat every day? How many daysdo we need to get through to get
through the winter before we cangrow more food. So you need to
(17:22):
be able to count and add andmultiply to know how much food
you need to store for thewinter, which will take you to
how much you need to grow in thesummer, which will take you back
to how much you need to plantand how many plants you think
the animals are going to eatbefore you get to have them. So
how much more do you actuallyneed to plant to be able to have
(17:43):
enough to harvest... and, uh oh,there's a new baby in the
family. Now you have to do that,but for five people, so you have
to be able to do that math inorder to survive, and even if
we're not thinking about growingall of our own food now, as
families, we have to figure outhow to budget, how much money we
need, how much money we need ifwe also want to go on vacation
(18:05):
to the beach at some point. Somath is really important, and we
do like it because it helps usget the things that we want and
need, even if we think, or somepeople think they don't like
math in school.
Dr. Melania Alvarez (18:18):
You're absolutely right.
Jane (18:20):
Zoe lives in California and is seven and wonders, why do
you need to do math? We alreadysaid math has helped people
survive, but what are some ofthe other ways math is needed?
Dr. Melania Alvarez (18:30):
Well, you need to do math for for so many
things. You need to do math togo to the supermarket. You need
to do math to trade with people.You need to do math, to build a
house, to build a pyramid, tostudy chemistry, to read graphs
about how, who's going to winthe presidential election. So we
(18:52):
also need to know, like, forexample, if you are in class and
you want to go to recess and youwant to know how many minutes
are there to recess? So you cancount them. Oh, it's almost
almost five minutes to recess, Iwant to go there. Also, if you,
if you like, to trade cards. Howmany cards should I trade for
this card? That card is worththree of these cards. And now,
(19:12):
for example, all thistechnology, the phones, the TVs,
everything, all of that wascreated thanks to math.
Saanvi (19:21):
My name is Saanvi. I'm 10 years old, and I live in
Bothell, Washington. Is theremath in everything?
Dr. Melania Alvarez (19:27):
Math is not just in everything. Math is also
a way to see everything. We cansee it in patterns from nature,
flowers. There's a sequencecalled the Fibonacci sequence
that goes one one, and then whatis one plus one, is two. And
then one plus two is three. Andthen if I add two and three, so
(19:48):
I take the last two numbers andadd them up, and then I get the
next sequence. And what'sinteresting is that that
sequence represents a lot ofthings that happen in nature,
the petals in flowers, theyusually, they are Fibonacci
number. So the really math islike this invisible thread that
(20:09):
connects everything around you,and it is the spiral in the
shell. We have the rhythm inmusic, when you bounce a
basketball, too. The trees inthe branches. But the secret
about this is you can see thisif you are curious. You have to
be curious, okay, to see it. Somath doesn't necessarily scream
(20:30):
for attention. It whispers toyou, says, hey, hey, come check
it out. Well, you have to becurious. You can notice a lot
more if you're curious, and youcan have a great time if you're curious.
Jane (20:44):
Well, you came to the right place, because anybody
who's listening to this podcastis a curious kid. It's in the
name of our show. So all of thekids who are listening, that's
something that we all have incommon all around the world. We
are curious kids who want toknow more about the world. So if
you have us convinced. Let'swrap up with Alistar's question.
Alistar (21:05):
Hi, my name's Alistar. How do you become a
mathematician?
Jane (21:10):
How do you become a mathematician? We all want to do
it now, Melania, how do webecome mathematicians?
Dr. Melania Alvarez (21:15):
So first of all, we are all mathematicians.
You know babies, theyimmediately can recognize
patterns. When we are playingand we're putting cubes on top
of each other and trying tomeasure if it's going to fall or
not fall, you know, and how tobuild things when we're little,
we are all mathematicians, allof us. When we like to say, How
(21:36):
many cookies I need to bake foreverybody in my family, I look
at cool pattern, I say, Oh, howdoes that grow? How can I
continue this pattern, all ofthat. Now, mathematicians, a
real mathematician, not justanswer the questions, they also
ask questions. A mathematicianis always asking questions about
how things work, and then triesto answer it. So this is what it
(21:59):
is. Everybody, you know,everybody can do math, and we
all can be mathematicians. Now,if what you want... asking is,
how I become a professionalmathematician, usually, most
mathematicians, I mean, thereare some who don't, but most of
them go to university, andthey... they have become
undergraduates in math or a mathrelated thing, and then they go
(22:21):
for a PhD in mathematics, andthey solve problems. Now there
are two types of mathematicians,mainly. The applied
mathematician and the puremathematician. So I am an
applied mathematician and myhusband is a pure mathematician.
So an applied mathematicianpeople come with problems to me,
like I have worked with problemsin anthropology. I have worked
(22:43):
with problems in engineering. Soengineers come with a problem
and they want, you know, theywant someone who does all the
calculations and who creates amodel of what they're seeing. So
I do that. So people comes withtheir problems, and I take care
of their math problems, onlytheir math problems. So that's
right. The pure mathematicians,they ask questions if some
(23:06):
really abstract thing can workor not work, you know, and then
they start, they start workingon the on this abstract
mathematics that it looks likethey are useless, that who
cares, doing this math, thatthere doesn't seem to be real
did he originally have?
application. And lo and behold,10 years from now, 200 years
from now, 3000 years from now,all of the sudden we find the
(23:28):
application. Isn't it.. it'slike magic, and that's what is
so exciting about math.
Jane (24:21):
So I want anybody who's listening now who wants to solve
it to pause the episode and seeif you can figure it out.
Can we go through the answer andhow one way that we might be
(24:42):
able to solve it, because I wasthinking about it while you were
talking, and I think I have ananswer.
Dr. Melania Alvarez (24:47):
Okay, why don't you tell me what you're
thinking about?
Jane (24:50):
Okay, I think he had seven chickens at the start.
Dr. Melania Alvarez (24:54):
And how did you solve that?
Jane (24:55):
When you said all the chickens were alive and at the
end he had no chickens, it mademe realize that when he at the
very end at the last market, hesold half of his chickens plus
half a chicken, he would have tohave one chicken to sell,
because no chickens were harmed.
Dr. Melania Alvarez (25:15):
Yes.
Jane (25:16):
So then I sort of went from the very end to the
beginning by sort of adding andmultiplying rather than
subtracting and dividing. And soI think he had one chicken at
the beginning,
Dr. Melania Alvarez (25:29):
Yes.
Jane (25:30):
Three chickens in the middle and seven chickens at the
start.
Dr. Melania Alvarez (25:34):
And you got it absolutely correct.
Jane (25:36):
Wow, phew.
Dr. Melania Alvarez (25:37):
And that's actually, that's the way,
working backwards, you see. Soyou work backwards. You said,
Okay, I think that the first oneis one, and then the next one
will be three, because I willbe, calculating what's half, you
know, double of that, and thenyou calculate what will be sold,
and then that. So you gotabsolutely right. So in the
first market, he has sevenchickens, and half of those
(25:57):
chickens is three and a halfplus half a chicken is four
chickens. So seven minus four isthree. So we're left with three
chickens. He goes to the secondmarket, half of those three
chickens is one and a halfchickens. And then plus half a
chicken, that's two chickens.Three minus two is one. So we're
(26:18):
left with one chicken. And thelast market is one chicken, and
then it's half of a chicken ishalf, and then the other half is
one. And there we are, and oh,there were no chickens hurt in
this puzzle.
Jane (26:33):
I was so, as you said, I was so pleased when I realized,
oh, I can figure this out andget to the answer.
Dr. Melania Alvarez (26:40):
So there are many ways that you can solve
a math problem. You can you canguess, and you can do a
systematic guess, not justrandom numbers, but little by
little, guesses that will giveyou some information. So you go
on. You can start backwards. Youcan draw a diagram, too.
Sometimes you can draw apicture, and that will help you.
There are many ways, and that'swhat mathematicians use. They
(27:01):
have the different ways ofapproaching and see what work,
what will work, and sometimes itworks, and if it doesn't work,
then you start again. And that'sall there is.
Jane (27:09):
Let's end this episode there. Did you figure out the
answer to the puzzle? I willadmit it took me a while, and I
had to write myself some notes,and I did start to get really
worried at one point that Iwasn't going to get the answer
right. And then my mind startedto go blank, and then I thought
of all of you listening, and Ithought, oh no, you'll all be so
disappointed in me, or think I'mnot very smart. But as Melania
(27:34):
was talking, I realized twothings. The first was that I
just needed to take a deepbreath and start working
backwards, and I could probablyfigure it out. And number two,
that if I couldn't figure itout, that's okay. No one is
supposed to just automaticallyknow all the answers to things.
And when we're learning math,part of what we're doing is
(27:55):
learning how to solve problems.So I knew I could ask Melania
for help if I got stuck, and shewould steer me to the right
strategy. Thanks to Dr. MelaniaAlvarez of the University of
British Columbia and the PacificInstitute for the Mathematical
Sciences for answering all ofour math questions today. We're
going to add some math puzzlesand resources in the show notes
(28:18):
if you want more. As always, ifyou have a question about
anything, have an adult recordyou asking it on a smartphone
using an app like voice memos,then have your adult email the
file to questions@butwykids.orgBut Why is produced by Melody
Bodette, Sarah Baik and me, JaneLindholm at Vermont Public and
distributed by PRX. Our videoproducer is Joey Palumbo, and
(28:42):
our theme music is by LukeReynolds. If you like our show,
please have your adults help yougive us a thumbs up or a review
on whatever podcast platform youuse, we'll be back in two weeks
with an all new episode. Untilthen, stay curious.
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