Transcript: Rectangles | Mar 26, 1999

(music plays)

The opening slate pops up with a countdown timer from 10 seconds and the title “TVO’s Virtual Classroom. Get connected.”
The “V” in “Virtual” is a tick, the “A” in “classroom” is an at sign with an extended loop that turns into a power cord with a plug at the end, and the first “O” in “classroom” is a spinning globe.

Mister C sits in the studio. He’s in his mid-forties, with a dark beard and wavy black hair. He’s wearing glasses, a white T-shirt with the image of a painting and patterned suspenders.

Mister C says GOOD MORNING.
IT'S MISTER C AND WELCOME BACK.
THIS IS THE LAST SHOW OF 1998,
AND I HOPE YOU HAVE A GOOD TIME.
I'VE GOT A NUMBER
OF THINGS PLANNED.
AS USUAL, I'M GOING TO
START WITH A PROBLEM.
AND THE PROBLEM
TODAY IS THIS ONE:

A blue piece of paper under the title “How can you cut a cake into 8 pieces with only 3 cuts?” shows the drawing of a birthday cake. Mister C appears in a small window on the right bottom of the screen.

He continues NOW I WANT YOU TO THINK ABOUT
THAT FOR A MOMENT OR TWO.
I'M GOING TO LEAVE THE SLATE
UP THERE FOR A FEW SECONDS
BEFORE I ASK YOU TO PHONE IN
AND LET ME KNOW WHAT YOU THINK
YOU SHOULD DO.
REMEMBER, WHAT WE'RE TRYING
TO DO IS EXACTLY THREE CUTS
WITH A KNIFE, AND I
WANT EIGHT PIECES.
A LITTLE BIT TRICKY, I THINK.
I WONDER IF IT'S DOABLE.
NOW, IT LOOKS LIKE WE HAVE
SOMEBODY THAT'S ABOUT READY
TO PHONE IN ALREADY,
SO I THINK --

He speaks with a spectator via a telephone conversation.

Alex says HELLO?

He says HI, IS THIS ALEX?

Alex says YES.

He says HI, ALEX.
HOW DO YOU THINK I COULD
POSSIBLY CUT THIS CAKE ONLY
THREE TIMES AND
GET EIGHT PIECES?

Alex says CUT ONE STRAIGHT
THROUGH THE MIDDLE.

He says OKAY, SOMETHING LIKE THIS.

He slides his index finger along the drawing.

Alex says YEAH.

He says YEAH.

Alex says AND THEN ONE
STRAIGHT ACROSS.

He says YEAH.

Alex says AND THEN ONE DIAGONALLY.

He says DIAGONALLY.
LIKE THIS?

Alex says YUP.

He says OH, I SEE, YEAH.
YOU KNOW, THERE'S A
POSSIBILITY THERE, ALEX.
I'M GOING TO SHOW YOU LATER
ON AND SEE HOW CLOSE YOU ARE.
BUT THAT SOUNDS
VERY, VERY CLOSE.

Alex says OKAY.

He says I'M GOING TO TAKE
ANOTHER CALL, IF THERE IS ONE.
HAS ANYBODY ELSE
GOT A SUGGESTION?
I WOULD LOVE TO TAKE
MORE SUGGESTIONS.
WELL, YOU KNOW, LET'S SEE, WE
GOT ANOTHER CALL COMING IN.

Sarah says HELLO?

He says HI, SARAH?

Sarah says YEAH.

He says WHAT DO YOU THINK
WE SHOULD DO?

Sarah says THE THREE CUTS, I THINK
YOU SHOULD PUT A LINE
THROUGH EACH ONE.

He says WHEN YOU SAY, “A LINE
THROUGH EACH ONE,”
NOW, I'M GOING TO
DO SOMETHING HERE.
LOOK AT THAT.
I GOT A -- THERE
YOU ARE -- A MUFFIN.
IT'S KIND OF A CAKE.
WHEN YOU SAY, “A LINE THROUGH
EACH ONE,” WHAT DO YOU MEAN?
LIKE A CUT LIKE THIS?

He places a knife on top of the muffin.

Sarah says YEAH.

He says AND THEN WHAT DO I DO?

Sarah says WELL, YOU
HAVE THREE CUTS.

He says YEAH.

Sarah says AND YOU PUT A LINE
THROUGH EACH ONE SO
IT CAN BE TWO.

He says A LINE
THROUGH EACH ONE.
I'M NOT SURE EXACTLY
WHAT YOU MEAN.

Sarah says WELL, THERE'S THREE.

He says YEAH.

Sarah says AND YOU TAKE...
OR YOU CUT...
CUT IT IN THREE.

He says YEAH, I'M NOT GOING
TO CUT UNTIL I SHOW YOU...
YOU SEE, I GOT TO BE...
MAKE SURE YOU'VE GOT
THE RIGHT ANSWER.
I'M NOT ACTUALLY GOING
TO CUT THIS MUFFIN YET.
SO IF I CUT THROUGH THIS
WAY, ALL THE WAY THROUGH,
THEN WHAT DO I DO?

Sarah says THEN YOU MAKE
ANOTHER LINE THE OTHER WAY.

He says YEAH, LIKE THIS, SAY.

Sarah says AND THEN ANOTHER
ONE LEFT TO RIGHT.

He says LIKE THIS?
LIKE THAT?

Sarah says YEAH.

He says OKAY.
YOU'VE GOT THE SOLUTION AND
ALEX MAY HAVE BEEN TELLING ME
THE SAME THING, SO I'M GOING
TO ACTUALLY DEMONSTRATE
BECAUSE YOU'VE GIVEN ME A
SOLUTION, I THINK, THAT WORKS.
LET'S TAKE A LOOK.
IF I CUT THIS WAY.
SO THERE'S ONE CUT.

Sarah says YEAH.

He says THEN I CUT THIS WAY.
HOW MANY PIECES HAVE WE GOT?

Sarah says FOUR.

He says NOW, LET'S
SEE IF I CAN DO THIS.
IT'S GOING TO BE A LITTLE
BIT MESSY, BUT I THINK
I'VE GOT IT HERE.

First he cuts the muffin making a cross and then through the middle.

He continues ONE, TWO, THERE WE ARE.
THERE'S A FEW CRUMBS
THAT WE CAN'T COUNT.
ONE, TWO, THREE, FOUR,
FIVE, SIX, SEVEN, EIGHT.
RIGHT ON.
THANK YOU VERY MUCH, SARAH.

Sarah says OKAY.

He says OKAY.
AND, IN FACT, I'VE GOT ANOTHER
LITTLE GRAPHIC THAT SHOWS
THE SAME THING.
THERE YOU ARE, AND THAT'S
THE ONE WAY OF DRAWING.

He grabs a sheet of paper that features a circle with two knifes in a cross position. It reads “1. Top view.” A rectangle with a knife placed in a vertical position reads “2. Side view.”

He continues SO IT IS INTERESTING THAT IT
CAN BE DONE, BUT THE IDEA IS
THAT YOU GOT TO REMEMBER
YOU'RE WORKING IN THREE
DIMENSIONS; THEREFORE, THAT
SLICE THROUGH THE SIDE IS THE
ONE THAT WE'RE MISSING.
NOW, YOU KNOW, IT'S JUST...
AS IT TURNS OUT, WE'RE AT THE
POINT WHERE I'VE GOT A PHONE
CALL COMING IN FROM ONE OF
THE KIDS THAT LIVES UP ON
MANITOULIN ISLAND, AND
IT'S ACTUALLY SOLANGE.
SO I'M JUST CHECKING TO
SEE IF SHE'S ON THE LINE.
HI, SOLANGE.
ARE YOU THERE?

Solange says HELLO, MISTER C.

He says IT'S BEEN A WHILE
SINCE WE'VE HAD A CHAT.
I UNDERSTAND YOU'VE BEEN
INVOLVED IN QUITE A MYSTERY.
CAN YOU TELL ME A
LITTLE BIT ABOUT IT?

Solange says IT'S BEEN REALLY NEAT.
SIMON AND I ARE REALLY LUCKY.
WE HAVE TWO NEW FRIENDS,
SWIFT ARROW AND RUNNING BEAR,
AKA SARAH AND DANIEL.
WE MET ON THE SHORE OF
GEORGIAN BAY AFTER THE BIG
POW-WOW AND, WELL, THEY HAVE
LET US BE PART OF A REALLY
NEAT RITUAL.

He says WHAT KIND OF A RITUAL?

Solange says IT SEEMS TO BE THAT
SARAH AND DANIEL GO FROM BEING
JUST KIDS TO BEING FULL
MEMBERS OF THE TRIBE,
KIND OF LIKE
BECOMING AN ADULT.

He says THAT'S PRETTY IMPRESSIVE.
SO WHAT DO YOU HAVE TO DO?

Solange says WELL, THE FOUR OF US HAVE
PLOTTED POINTS ON A MAP
OF MANITOULIN ISLAND.
EACH WEEK, WE HAVE TO FIND A
ROCK CAIRN IN WHICH WE FIND,
BELIEVE IT OR NOT,
A MATH ASSIGNMENT.
I HAVE A VIDEO CLIP
HERE OF A ROCK CAIRN.
SHOULD I RUN IT?

He says SURE, BY ALL MEANS.

Solange says OKAY, HERE GOES.

A clip plays. It shows a stone sculpture.

He says THIS IS A TRADITIONAL
INUIT MARKER AND SOMETIMES
YOU WOULD FIND SUPPLIES UNDER
IT OR PERHAPS YOU MIGHT EVEN
FIND IT MARKS THE WAY TO GO
FROM ONE PLACE TO ANOTHER.
SO THIS IS WHAT A ROCK
CAIRN MIGHT LOOK LIKE.

The clip ends.

Solange says WE'RE SUPPOSED TO
SOLVE ALL THE QUESTIONS AND,
BY FEBRUARY, PUT ALL THE
PIECES OF THE PUZZLE TOGETHER.

He says CAN I HELP AT ALL?

Solange says WELL, EVERY SO OFTEN,
WE'VE RUN INTO SOME TOUGH
PROBLEMS, AND WE NEED
A LITTLE BIT OF HELP.

He says WELL, I'LL
TELL YOU WHAT.
JUST TUNE INTO THE VIRTUAL
CLASSROOM ACTUALLY.
I'VE GOT A WHOLE BUNCH OF
KIDS THAT HAVE VOLUNTEERED,
ABSOLUTELY VOLUNTEERED
TO HELP YOU OUT.

Solange says THAT'LL BE GREAT.
THANKS A WHOLE BUNCH.

He says BYE, SOLANGE.
KEEP IN TOUCH.

Solange says BYE.

He says GEE, IT'S REALLY GREAT
TO TALK TO HER AND SORT OF
BRING US UP TO DATE WHERE
WE ARE IN THE MYSTERY.
MAYBE LATER IN THE
PROGRAM I MIGHT COME BACK TO
IT FOR A MOMENT OR TWO
IF WE HAVE THE TIME.
BUT THIS IS THE POINT IN THE
PROGRAM WHERE I'D ACTUALLY
LIKE TO TAKE UP THOSE STRAW
PROBLEMS, AND I'M GOING TO DO
THEM ONE AT A TIME AND TRY
TO DO AS MANY AS I CAN
IN THE TIME ALLOWED.
HOWEVER, I DO HAVE A
QUESTION THAT I REALLY
WANT TO GO TO FIRST.
AND WE'RE GOING TO GET
IT UP HERE ON THE BOARD.
THERE WE ARE.
NOW, THIS IS BASED
ON YOUR HOMEWORK.

A caption appears on screen under the title “Question Number 1.” It reads “Which two straw problems could not be solved (in 2 dimensions)? 1: 4 and 5. 2: 6 and 7. 3: 7 and 8. 4: 8 and 9.” A gray bar graph reads “0 per cent.”

He continues WHICH OF TWO STRAW PROBLEMS
COULD NOT BE SOLVED,
AND I PUT IN BRACKETS
THERE, IN TWO DIMENSIONS.
I HAD TO BE
CAREFUL ABOUT THAT.
NOW, I NEED A
FEW ANSWERS HERE.
I NEED A LOT OF PEOPLE
TO PHONE, OR DIAL IN.
PRESS ONE IF YOU
THINK FOUR AND FIVE.
THAT'S IT.
WE'RE BEGINNING
TO GET PEOPLE NOW.
PRESS TWO IF YOU THINK IT'S
PROBLEMS SIX AND SEVEN.
WE NEED A FEW MORE.
WE'RE A LONG WAY AWAY.
NUMBER THREE, PRESS THREE IF
YOU THINK IT'S PROBLEMS
SEVEN AND EIGHT.
WE'RE BEGINNING TO
GET SOME PEOPLE NOW.
THIS IS BETTER.
WHEN I GET UP TO 50 PERCENT,
THEN I'LL BE REALLY HAPPY.
WE'RE AT 24 PERCENT.
SO WHAT DO YOU THINK?
COME ON, A FEW MORE PEOPLE.
THERE'S A COUPLE MORE.
THAT'S IT.
WE'RE GETTING THERE NOW.
NOW, JUST WAIT A
MOMENT OR TWO MORE.
THAT'S ONLY A THIRD OF YOU THAT
HAVE PHONED IN APPROXIMATELY.

The bar graph changes to blue as numbers go up from “3 per cent” to “33 per cent.”

He continues OKAY, I'M GOING TO SHOW YOU
THE GRAPH, AND I'M NOT GOING TO
TELL YOU THE CORRECT ANSWER
BECAUSE WE'RE GOING TO FIND
OUT WHEN WE TAKE
UP THE PROBLEMS.

A four-bar graph appears. A green bar reads “1,” a purple bar reads “2,” a blue bar reads “4” and a red bar reads “11.”

He continues BUT THE MAJORITY OF YOU CHOSE
NUMBER FOUR, WHICH IS EIGHT
AND NINE, SO LET'S SEE
IF YOU WERE RIGHT OR NOT.
OKAY.
WHAT WE'RE GOING TO DO IS I'M
GOING TO DO THE STRAW PROBLEMS.
I'VE GOT THEM ALL SET UP HERE,
AND I'M GOING TO GET YOU TO
PHONE IN AND GIVE ME THE
ANSWERS AS WE GO ALONG.
THE VERY FIRST ONE WAS, ADD
TWO STRAWS TO THE THREE SHOWN
TO MAKE THE NUMBER EIGHT.
SO I'VE GOT ONE, TWO, THREE
STRAWS, THERE THEY ARE.
AND I HAVE TO ADD TWO TO
MAKE THE NUMBER EIGHT.

A blue sheet of paper reads “Straw problems. 1: Add two straws to the three shown to make eight. 2. Remove two straws to leave two squares.” First, it shows three sticks and then a dotted square with two dotted perpendicular lines inside.

He continues SO WE'LL TAKE A CALL.
LET'S SEE.
WE'LL TRY DANIELLE
FROM TRILLIUM.

Danielle says HELLO?

He says HI, DANIELLE.

Danielle says HI.

He says OKAY, WHAT DO I DO?
I ADD TWO.
WHAT DO I DO WITH THEM?

Danielle says OKAY, YOU GOT TO
PUT ONE ON THE TOP.
LIKE, SWITCH THE...
YEAH, LIKE THAT.
AND THEN YOU PUT THE
OTHER ONE ON THE RIGHT.
LIKE, NO, ON THE BOTTOM.

He says OKAY.
TALK DIRECTLY INTO
THE PHONE SO...

Danielle says OKAY, YOU PUT ONE
ON THE BOTTOM.
THAT ONE ON THE BOTTOM.

He says YEAH.

Danielle says AND THEN YOU PUT THE
STRAW ON THE LEFT...

He says YEAH.

Danielle says IN THE MIDDLE.

He says OH I SEE WHAT
YOU'VE DONE HERE.

Danielle says AND THEN IT
MAKES THE LETTER...
THE NUMBER EIGHT.

He says HEY, I'M GOING TO
TAKE THAT AS A SOLUTION.
I'LL TELL YOU WHAT.
I'LL LOOK FOR ANOTHER
SOLUTION AS WELL, BUT HEY,
THAT'S ONE.
GOOD FOR YOU.
OKAY, LET'S SEE.
LET'S GO TO...
OKAY.

Dan says HELLO?

He says HELLO, DAN?

Dan says YUP.

He says OKAY, WHAT DO YOU
THINK I SHOULD DO?

Dan says TAKE THE TWO
ORANGE ONES AND MAKE
A 'V' AT THE BEGINNING.

He says AT THE
BEGINNING, RIGHT.
I ALMOST PUT IT AT THE
WRONG END, DIDN'T I?
AND HOW IS THAT EIGHT?

Dan says IT'S IN ROMAN NUMERALS.

He says THANK YOU VERY MUCH.
OKAY, SO WE SOLVED THAT ONE,
AND I'M GOING TO MOVE TO
NUMBER TWO NOW, AND IT
SAYS, REMOVE TWO STRAWS
AND LEAVE TWO SQUARES.
NOW, I THINK, AFTER
WHAT WE DID LAST WEEK...
AND I'M GOING TO GET...
LET'S SEE IF WE CAN
GET SOME PHONE CALLS.
HOW DO WE SOLVE
NUMBER TWO HERE?
REMOVE TWO STRAWS AND
LEAVE TWO SQUARES.
WE DID SOMETHING
LIKE THIS LAST WEEK.
OKAY, SOMEBODY FROM...
I THINK IT'S...
WHO ARE WE CONNECTING TO?
SARAH FROM ELGIN?

Sarah says HELLO?

He says HI.
IS IT SARAH
OR LINDSAY?

Sarah says IT'S SARAH.

He says OKAY, GREAT.
WHAT DO I DO?

Sarah says YOU MOVE THE MIDDLE
SQUARE ON THE BOTTOM,
THE RED ONE.

He says YEAH, OKAY.

Sarah says AND THEN...
SO ONE THAT JUST MOVED.

He says OH, YEAH, OKAY.
WELL DONE.
THANK YOU, SARAH.

Sarah says OKAY.

He says OKAY, WE'RE GOING
TO MOVE TO...
LET'S SEE.
THIS ONE.
REMOVE FOUR STRAWS
TO LEAVE SIX.
AND I'LL SET IT UP AS QUICKLY
AS I CAN WHILE WE'RE GETTING
CONNECTED HERE.

Another piece of paper reads “3. Remove four straws so that six squares remain. 4. Add five straws to these to make nine.” It shows a square made of nine dotted smaller squares and then six sticks.

He continues IT'S THE PROBLEM WITH THESE
STRAWS, THEY MOVE AROUND
A LITTLE BIT.
OKAY, WE'RE COMING ALONG.
HELLO.
IS IT... WE'RE BACK TO
SARAH AT TRILLIUM, I THINK.

Sarah says HI.

He says HI.
HOW ARE YOU DOING?

Sarah says GOOD.

He says WE JUST TALKED A LITTLE
WHILE AGO, DIDN'T WE?

Sarah says YEAH.

He says OKAY, GREAT.
NOW, I'VE ALMOST GOT
THIS SET UP AND I...
LUCKILY, I HAVE ENOUGH STRAWS.
TELL ME WHAT I NEED TO DO.

Sarah says LET ME JUST FIND IT.

He says OKAY.
WELL, IT'S QUESTION NUMBER
THREE, SO IT'S REMOVE FOUR
STRAWS SO THAT WE END
UP WITH SIX SQUARES.

Sarah says OKAY.
YOU TAKE AWAY THE TOP,
THE SECOND TOP ONE.

He says UP HERE?

Sarah says NO.
THE... ON THE RIGHT.
ON THE LEFT, I MEAN.

He says UP HERE?

Sarah says DOWN ONE.

He says THIS ONE?

Sarah says NO.
YEAH, THAT ONE.

He says YEAH, THE ORANGE ONE?

Sarah says YEAH.

He says GOTCHA.

Sarah says AND TAKE THE OTHER
ONE RIGHT BELOW IT AWAY.

He says YEAH.

Sarah says THEN ON THE
OTHER SIDE, ON...
GOING TO THE RIGHT SIDE.

He says LIKE THAT ONE?

Sarah says YEAH.

He says GREAT.
WHAT ELSE?

Sarah says AND THEN THE NEXT ONE.

He says LET'S SEE.
HOW DO YOU GET SIX
SQUARES OUT OF THAT?
TELL ME.
DESCRIBE THE SQUARES.

Sarah says THERE IS ONE...
THERE'S TWO SQUARES...
FOUR SQUARES THERE AND...

He says ONE, TWO,
THREE, FOUR, RIGHT.

Sarah says FOUR SQUARES THERE
AND TWO SQUARES ON...

He says ONE BIG
ONE HERE, RIGHT?

Sarah says YEAH.

He says AND THEN ONE
REALLY BIG ONE HERE.

Sarah says YEAH.

He says WELL DONE.
THANK YOU VERY MUCH.

Sarah says YOU'RE WELCOME.

He says OKAY, LET'S
DO THIS NEXT ONE.
ADD FIVE STRAWS TO MAKE NINE.
BOY, THIS IS A TOUGH ONE.
ADD FIVE STRAWS TO MAKE NINE,
AND THAT SEEMS TO ME FIVE AND
SIX MAKES 11, BUT YOU KNOW.
THERE MUST BE A
WAY OF DOING THIS.
OKAY, THERE WE ARE.
WE'VE GOT ALL THE
STRAWS KIND OF LINED UP.
YEAH, THAT'S IN A GOOD SPOT.
SO WE'RE MAKING A CONNECTION.

He places four yellow straws and two red ones, one next to the other.

He continues IT'D BE GOOD TO GET SOMEBODY
FROM ELGIN OR FROM USBORNE.
I'D LOVE TO TALK TO
SOMEBODY FROM USBORNE.
AND I THINK WE'RE GOING TO
TRY TO CONNECT TO JENNIFER,
SO HANGING IN TIGHT HERE.

Jennifer says HELLO?

He says HI.
IS THIS JENNIFER?

Jennifer says YEAH.

He says OKAY, WHAT DO I DO TO
MAKE THIS INTO NINE?

Jennifer says YOU HAVE TO SPELL,
LIKE, THE WORD 'NINE'.

He says OH.
WELL, HOW DO I DO THAT?
START WITH...

Jennifer says YEAH.

He says AN N, OKAY.

Jennifer says AND THEN...

He says THAT'S AN I.

Jennifer says I, AND THEN
ANOTHER STRAW.

He says ANOTHER STRAW, SO THAT'S
THE SECOND ONE I'VE PUT IN.

Jennifer says AND THEN, LIKE,
AN E MAKES THREE.

He says HEY, THAT EVEN LOOKS
GOOD ON THE TV, I THINK.

Jennifer says YEAH.

He says WELL DONE.
THANK YOU VERY MUCH.
HEY, WE GOT FOUR SOLVED.
WE'RE GOING GREAT GUNS HERE.
LET'S SEE.
NOW, THIS IS KIND OF A TWO,
THREE-PARTER, SO WHAT WE'RE
ASKING IS WHAT THE MINIMUM
NUMBER OF STRAWS IS TO MOVE
FROM THIS TO THIS.

A blue sheet of paper reads “5. What is the smallest number of straws you need to move to convert this shape into each of the others?” It shows the typical drawing of a house from four different perspectives.

He continues SO I'LL QUICKLY SET UP
AND I'M SETTING UP HERE.
NICE THING ABOUT THESE IS
THAT, ONCE AGAIN, IT'S SET UP
FOR THE ONE AND IT'S
ALL, IT'S SET UP FOR
ALL OF THEM REALLY.
SO WE GOT...
MAKING A HOUSE,
AND THERE WE ARE.
OKAY.
WE GOT SOMEBODY CONNECTING?
YES, WE GOT SOMEBODY
BEING CONNECTED.
KIND OF A HOUSE, I THINK.
HELLO.
AM I -- IS IT
BRITTANY OR GILLIAN?

Gillian says GILLIAN.

He says HI, GILLIAN.

Gillian says HI.

He says OKAY, WHAT DO I DO TO MOVE
THIS KIND OF A HOUSE INTO ONE
THAT LOOKS THAT OTHER WAY
WITH THE MINIMUM NUMBER?

Gillian says YOU MOVE ONE STRAW.

He says WHICH ONE?

Gillian says THE ONE AT THE
TOP IN THE MIDDLE.

He says NOT THIS ONE?

Gillian says NO.
IT'S... YEAH.
YEAH.

He says LIKE THAT?

Gillian says YEAH.

He says HEY, SIMPLE AND EASY.
YOU'RE RIGHT ON.
THANK YOU VERY MUCH.
OKAY.
NOW, WHAT WE'RE TRYING TO DO
IS TO MAKE THIS ONE DOWN HERE,
WHICH IS LIKE TWO HOUSES,
SORT OF SIDE BY SIDE.
HOW MANY DO I NEED TO MOVE?
AND WE'RE GOING TO CONNECT TO
EITHER LINDSAY OR SARAH FROM
ELGIN, I THINK.

Sarah says HELLO?

He says HI.
IS IT LINDSAY OR SARAH?

Sarah says IT'S SARAH AGAIN.

He says HI, SARAH.
OKAY, WHAT DO I DO TO
MAKE THE DOUBLE HOUSE?

Sarah says YOU MOVE THE RED ONE ON
THE TOP DOWN DIAGONALLY,
LIKE THAT.

He says LIKE THAT?

Sarah says YEAH.

He says HEY, THAT
ONE WAS PRETTY EASY.
WELL DONE.
OKAY, THAT LEAVES
THE OTHER ONE.
NOW, THIS IS A
DIFFERENT KIND OF HOUSE.
THIS ONE'S GOT A FLAT
ALONG THE BOTTOM.
THIS ONE IS KIND OF A
PERSPECTIVE VIEW, THIS NUMBER
C HERE.
THE QUESTION IS, HOW MANY
STRAWS DO I ACTUALLY HAVE TO
MOVE TO -- MINIMUM NUMBER OF
STRAWS DO I HAVE TO MOVE
TO ACTUALLY MAKE THE CHANGE?
SO LET'S SEE.
WE'RE MAKING ANOTHER
CONNECTION HERE.
WE'RE ROLLING THROUGH
NUMBER FIVE FAIRLY QUICKLY.

Gillian says HELLO?

He says HELLO.
WHO AM I TALKING TO THIS TIME?
IS IT GILLIAN?

Gillian says YEAH.

He says OKAY, WHAT DO I DO?
HOW MANY STRAWS DO I ACTUALLY
HAVE TO MOVE THIS TIME?

Gillian says YOU HAVE TO MOVE
FIVE STRAWS.

He says RIGHT.
WHICH FIVE?

Gillian says OKAY, THE ONE AT THE
BOTTOM, THE BOTTOM RIGHT.

He says THE BOTTOM RIGHT.
SURE ABOUT THAT?
THIS ONE?

Gillian says YEAH.
LIKE, YOU MOVE IT UP.
LIKE, YOU TURN IT UP.

He says OH I SEE WHAT
YOU'RE GOING TO DO.
CAN I HELP YOU OUT A
LITTLE BIT ON THIS ONE?
WHEN YOU SAID,
'FIVE', IT'S CORRECT.
TAKE A LOOK AT THIS PART
OF THE HOUSE IN HERE.
NOTICE THAT IT'S ALREADY
BUILT HERE, SO DO YOU REALLY
WANT TO MOVE ANY
OF THESE GUYS?

Gillian says NO.

He says BECAUSE
THEY'RE ALREADY BUILT.
THE ONES YOU WANT TO MOVE
ARE OVER ON THIS SIDE.

Gillian says OKAY.

He says AND I THINK ONCE YOU DO
THAT, THEN YOU SEE THAT...
WHAT YOU DO IS YOU TAKE THESE,
YOU PUT THEM ON ANGLES
LIKE THIS, RIGHT?

Gillian says YEAH.

He says AND THEN WE GET
THE DESIRED RESULT.
THANK YOU VERY MUCH.

Gillian says OKAY.

He says NUMBER SIX.
TWELVE STRAWS FORM
THREE SQUARES.

He grabs another sheet of paper that reads “6. Twelve straws form three squares. Move three straws to make an arrangement with five squares.” The paper features one dotted square, then another one to the right but in a lower position and a third one to the right placed at the same level as the first one.

He continues MOVE THREE STRAWS TO MAKE AN
ARRANGEMENT OF FIVE SQUARES.
OKAY, SO THIS IS RELATED TO
ONE OF THOSE OTHER ONES,
SO WE SHOULD BE ABLE TO GET
THE ANSWER REASONABLY QUICKLY,
I HOPE.
LET'S SEE.
IF I GO IN THAT DIRECTION,
I THINK I'M SAFE.

Sarah says HELLO?

He says WHO AM I TALKING TO?
IS IT SARAH OR GREG?

Sarah says SARAH.

He says HI.

Sarah says HI.

He says NOW, I'VE JUST
ABOUT GOT THIS SET UP.
ONE MORE TO PUT ON HERE.
SO I'M MOVING HOW
MANY OF THEM, THREE?

Sarah says YUP.

He says OKAY, WHAT THREE?

Sarah says OKAY, YOU MOVE THE RIGHT
ONE, THE LAST RIGHT ONE, YEAH.

He says OKAY.

Sarah says YOU MOVE IT IN THE MIDDLE
BETWEEN THE TWO TOP ONES.

He says YEAH, LIKE THAT?

Sarah says YEAH.
AND THEN YOU MOVE
THE BOTTOM ONE.

He says WHICH ONE?

Sarah says THAT ONE.

He says YUP.

Sarah says AND THEN YOU MOVE
IT BESIDE THE LEFT.
YEAH, RIGHT THERE.
AND THEN YOU MOVE THE
OTHER ONE ON TOP OF THAT.

He says FIVE SQUARES.
THANK YOU VERY MUCH.

Sarah says YOU'RE WELCOME.
BYE.

He says BYE-BYE.
OKAY, WE'RE STILL ROLLING.
FIVE STRAWS.
WE MOVE FIVE OF THEM TO
CREATE A PATTERN OF THREE
IDENTICAL SQUARES.

A new piece of paper reads “7. Move five straws to create a pattern of three identical squares.” The paper shows a dotted cross on top of a dotted square.

He continues SO IN OTHER WORDS, WE ACTUALLY
WANT SOMETHING THAT LOOKS
LIKE THE ONE THAT
WAS PREVIOUS TO THAT.
WHOOPS.
I'M GOING TO SLIDE OVER
HERE AND TRY TO AVOID MY...
OKAY, HERE WE GO.
AND WE'RE IN THE PROCESS
OF MAKING A CONNECTION.
I HOPE SOMEBODY'S PHONING IN
TO TELL ME HOW TO DO THIS ONE.
I'D LIKE TO SEE SOME
CALLS ON THIS ONE.
THERE ARE A WHOLE
BUNCH OF POSSIBILITIES.
THERE WE ARE.
I'M ALL SET UP.
BE NICE IF WE GOT A CALL
PERHAPS FROM USBORNE.
I'D LIKE TO GET MORE
CALLS FROM USBORNE.
THERE'S SOMEBODY.
THINK WE'RE TRYING TO
CONNECT TO JENNIFER.
WE'RE TRYING TO MOVE FIVE
STRAWS IN THE PATTERN TO GET
THREE IDENTICAL SQUARES.

Jennifer says HELLO?

He says HI.
IS IT JENNIFER,
EXCUSE ME?

Jennifer says YEAH.

He says OKAY, HOW DO I DO IT?

Jennifer says YOU MOVE...
YOU KNOW THAT RED STRAW UP
IN THAT, LIKE, LITTLE PLUS
SIGN THING?

He says OH, UP HERE?

Jennifer says NO, UP THERE.
YEAH.
YOU MOVE THAT,
MOVE IT AND PUT IT IN
THE MIDDLE THING, LIKE IN
THE MIDDLE OF THE SQUARE.
NO, DOWN THERE, LIKE...

He says HERE?

Jennifer says YEAH.

He says OKAY.

Jennifer says AND THEN YOU
MOVE THE OTHER ONE.

He says WHICH OTHER ONE?
THIS ONE?

Jennifer says YEAH.
AND MOVE THAT DOWN
THERE TOO, LIKE...

He says SORT OF IN THE SAME
DIRECTION AS THE ONE,
OR LIKE THIS?

Jennifer says YES.

He says LIKE THIS?

Jennifer says NO.
LIKE, DOWN.

He says LIKE THIS?

Jennifer says YEAH.

He says OKAY.

Jennifer says AND THEN YOU MOVE
THE ONE IN THE CORNER,
THE RED ONE.

He says THIS ONE?

Jennifer says YES, AND PUT
IT ACROSS, LIKE THERE.

He says YEAH.

Jennifer says AND THEN YOU
MOVE THE OTHER ONE.

He says THIS ONE?

Jennifer says YEAH, AND PUT IT
ACROSS THE OTHER WAY.

He says THAT WAY?

Jennifer says YEAH.

He says OKAY.
THERE ARE THREE SQUARES THERE.
WE GOT A COUPLE HANGING
OFF ON THE OUTSIDE HERE,
BUT YOU GOT THREE SQUARES.
WELL DONE.

Jennifer says OKAY.

He says I'M GOING TO SEE IF WE
CAN GET ONE MORE SOLUTION FOR
THAT, SO MAYBE WE CAN
COME BACK TO TRILLIUM.
THAT WAS A GOOD ONE.

Andrew says HELLO?

He says HELLO, AND I'M
SPEAKING TO CHRIS?

Andrew says NO, YOU'RE
SPEAKING TO ANDREW.

He says OH, SORRY ABOUT THAT.
OKAY, NOW, WHAT
STRAWS DO I MOVE?

Andrew says MOVE THE SAME
RED ONE IN THE CROSS.

He says YEAH.

Andrew says JUST STRAIGHT DOWN.

He says STRAIGHT
DOWN LIKE HERE?

Andrew says YES.

He says OKAY.

Andrew says AND THEN MOVE THE RIGHT
CORNER TOP TO THE SIDE.

He says OKAY, SO THE RIGHT...
THIS ONE?

Andrew says NO, THE OPPOSITE SIDE.

He says OVER HERE?

Andrew says YES.

He says GOTCHA.

Andrew says MOVE IT IN, PLEASE.

He says MOVE IT INTO HERE.

Andrew says YES.

He says OKAY, THAT'S
TWO MOVES, GREAT.
I THINK WE'RE GOING PRETTY
WELL HERE, I THINK.

Andrew says AND MOVE THE
YELLOW AT THE BOTTOM.

He says YUP.

Andrew says NO, THE OTHER SIDE.

He says THIS ONE?

Andrew says YES.

He says OKAY.

Andrew says MOVE THAT...
UP AND ACROSS.

He says UP HERE PERHAPS?

Andrew says YES.

He says OKAY.

Andrew says AND THE OTHER YELLOW ONE
BESIDE IT... ACROSS.

He says YEAH.

Andrew says AND THEN GO
UP TO THE VERY TOP.

He says WE GOT IT, I THINK.
RIGHT THERE, EH?

Andrew says YES.

He says THERE'S ANOTHER SOLUTION.
WELL DONE.
THANK YOU.
OKAY, WE'RE MOVING
RIGHT ALONG HERE.
NOW, NUMBER EIGHT, MOVE
THREE STRAWS TO GET THREE
IDENTICAL TRIANGLES.
NOW, LET'S SEE WHAT WE
CAN DO WITH THIS ONE.

A sheet of paper reads “8. Move three straws to create a shape consisting of three identical triangles. 9. Add three straws to the three below to create a figure with four identical triangles.” The paper displays a 3-D dotted cube leaning to one side and then a triangle.

He continues AND I THINK WE'RE GOING
TO TALK TO SOMEBODY
FROM USBORNE.

Jody says HELLO?

He says HI.
WHO AM I SPEAKING TO?
IS IT JOHN?
OR, EXCUSE ME,
JODY OR ZACH?

Jody says JODY.

He says SORRY ABOUT THAT.

Jody says THAT'S OKAY.

He says SOMETIMES I LOOK OUT
OF THE CORNER OF MY EYE
AND I SEE YOUR NAMES ON THE
COMPUTER SCREEN BUT, YOU KNOW,
IT GETS A LITTLE BIT
BLURRY IN THE MORNING.
YOU KNOW HOW IT IS.

Jody says YEAH.

He says OKAY.
WHAT CAN YOU TELL ME
ABOUT THIS PUZZLE?

Jody says OKAY, YOU MOVE THE
BOTTOM RIGHT YELLOW ONE.
THAT ONE, AND YOU MOVE IN
THE MIDDLE OF THOSE TWO.
LIKE, RIGHT THERE.
AND THEN YOU MOVE THE BOTTOM
ONE, AND YOU MOVE IT TO...
NO.
JUST A MINUTE.
OKAY, YOU MOVE THE TOP
LEFT ONE INTO THE MIDDLE.

He says THIS ONE?

Jody says TOP LEFT ONE
INTO THE MIDDLE.

He says LIKE THIS?

Jody says YES.

He says OKAY.

Jody says OKAY.
YEAH, LIKE THAT.

He says SOMETHING LIKE THAT?
OKAY.

Jody says THERE'S THREE TRIANGLES.

He says ARE THEY IDENTICAL?

Jody says OH, OKAY.

He laughs and says YOU'VE MADE A REALLY
GOOD ATTEMPT, BUT YOU SEE,
THIS ONE ACTUALLY IS
BIGGER THAN THESE.
IT'S HARD TO SET UP HERE
BECAUSE THE STRAWS MOVE AROUND
TOO MUCH.
I'LL TAKE ONE MORE CALL
ON THIS ONE AND...
YES, WE'RE GOING TO GO TO
SOMEBODY FROM TRILLIUM.
AM I SPEAKING TO DAVID?

David says YEAH.

He says HI, DAVID.
WHAT DO YOU THINK
ABOUT THIS ONE?

David says MOVE THE RED ONE IN
THE MIDDLE... DOWN.
NO, LIKE, KEEP IT THERE BUT
JUST MOVE IT VERTICAL A
LITTLE BIT MORE.
YEAH.
ACTUALLY, JUST LEAVE
IT THE WAY IT WAS.

He says LEAVE IT THE
WAY IT WAS, OKAY.

David says AND GO TO THE
BOTTOM FLAT ONE.

He says THIS ONE?

David says YEAH.
MOVE IT UP SO
IT'S STRAIGHT.

He says LIKE THIS?

David says YEAH.
MOVE IT TO THE OTHER YELLOW
ONE SO THEY'RE TOUCHING.

He says OH, YEAH, OKAY, GOTCHA.
SOMETHING LIKE THIS, RIGHT?

David says AND THEN SORT OF MOVE
IT SO THE STRAWS ARE MOVING
AGAIN, AT THE RED AND THE
YELLOW WHEN THEY MEET.

He says OH, OKAY.
SO, YEAH, YOU
MEAN THERE, RIGHT?
OKAY.

David says THEN AT THE TOP YELLOW ONE
ON THE SLANT TO THE RIGHT.

He says YEAH, OKAY.

David says SLIDE IT DOWN.

He says LIKE THAT?

David says NO.
LIKE, SWING IT VERTICAL.

He says OH, LIKE THIS?

David says YEAH.
AND THEN TIGHTEN THE
STRAWS ON THE SIDES AGAIN,
BUT LIKE... YELLOW MIDDLE...

He says GOTCHA, YEAH.

David says SO THEY'RE EVEN.

He says OH, I SEE WHAT
WE HAVE HERE.

David says AND THEN TAKE THE TOP
RED ONE, THE FLAT ONE.

He says YEAH.

David says MOVE IT DOWN SO
IT'S TOUCHING THE MIDDLE.
YEAH.
AND THEN...

He says OKAY, INTERESTING.
NOW, MY CHALLENGE HERE
IS ARE THOSE TRIANGLES
EXACTLY IDENTICAL?
AND WE DID DO SOME ADDITIONAL
LITTLE MOVES THERE.
I WANT YOU TO THINK ABOUT
THAT ONE A LITTLE BIT MORE.
I THINK, TECHNICALLY SPEAKING,
BECAUSE THE ANGLES IN THIS
PUZZLE, THAT IT'S IMPOSSIBLE
TO GET THE EQUILATERAL
TRIANGLES BECAUSE, REMEMBER,
THAT EACH ONE OF THESE IS
EXACTLY THE SAME LENGTH, SO
WHAT IT MEANS IS THAT YOU
END UP WITH EQUILATERAL
TRIANGLES, MEANING THAT ALL
THE ANGLES HAVE TO BE 60
DEGREES ON THE INSIDE.
THAT'S ONE OF THE ONES
THAT IS IMPOSSIBLE TO DO.
THE ONE BELOW IT.
NOW, THAT WAS A GOOD ATTEMPT
THAT WE GOT AND I THINK THAT
IT WAS AS CLOSE AS YOU'RE
GOING TO GET, BOTH PEOPLE THAT
MADE AN ATTEMPT HERE.
SO YOU'RE ADDING THREE
HERE TO MAKE FOUR.
ANYBODY KNOW WHAT THE
SOLUTION TO THIS ONE IS?
HI, CARRIE?
IT'S CARRIE OR TYLER?

Carrie says HELLO?

He says HI, CARRIE?

Carrie says HI.

He says OKAY, WHAT DO YOU DO TO
ACTUALLY SOLVE THIS ONE?

Carrie says PARDON?

He says DO YOU KNOW
HOW TO SOLVE THIS ONE?

Carrie says NO.

He says OKAY.

Carrie says IT'S IMPOSSIBLE.

He says YEAH, YOU'RE RIGHT, BUT
IT'S NOT TOTALLY IMPOSSIBLE.
NOW, REMEMBER, WHAT
DID I SAY WHEN I SAID
WHICH TWO COULD
NOT BE SOLVED?
DIDN'T I ADD A LITTLE
THING IN BRACKETS?
I SAID THAT IN TWO
DIMENSIONS, RIGHT?
NO PROBLEM.
WE'RE SPEAKING TO
NICK NOW, I THINK.
HI, NICK.

Nick says HI.

He says DO YOU KNOW A
SOLUTION TO THIS ONE?

Nick says IMPOSSIBLE.

He says IT'S IMPOSSIBLE ON THE
PLANE, BUT I'M GOING TO TELL
YOU THAT IT'S NOT
TOTALLY IMPOSSIBLE.
HAVE YOU EVER HEARD
OF A TETRAHEDRON?

Nick says YEAH.

He says A TETRAHEDRON IS
THREE DIMENSIONAL.
NOW, IN THREE DIMENSIONS,
WHOOPS, THIS IS GOING TO BE
HARD FOR ME TO DO.
BUT WHAT WE WOULD ACTUALLY
DO IS WE WOULD BUILD A
TRIANGULAR BASE PYRAMID.
I HAVEN'T GOT ENOUGH FINGERS
TO PUT IN THE LAST PIECE,
BUT THEN YOU WOULD GET FOUR
IDENTICAL TRIANGLES.
BUT THAT'S NOT IN
TWO DIMENSIONS.
IN TWO DIMENSIONS, IT'S
IMPOSSIBLE, BUT IN THREE,
IT
IS
POSSIBLE.
NOW, I'M GOING TO QUICKLY
GO THROUGH THE LAST COUPLE
BECAUSE I DO HAVE A LESSON.
ANYBODY KNOW THE
ANSWER TO NUMBER TEN?
MOVE ONE STRAW TO MAKE
THE EQUATION TRUE.

A blue sheet of paper reads “10. Move one straw to make this equation true.” The equation shows one vertical stick, a minus, three vertical sticks, an equal and two vertical sticks. Then, it reads “11. Move one straw to make this equation true.” The equation shows one vertical stick, a plus, two vertical sticks, a plus, three vertical sticks, an equal and four vertical sticks.

He continues ANYBODY KNOW THIS ONE?
SOMETIMES I HAVE TO THINK
ABOUT THE ANSWERS TO THESE
BECAUSE THEY'RE REALLY
GOOD LITTLE QUESTIONS,
AND THEY'RE GOOD THINKERS.
OKAY.

Alex says HELLO?

He says HI, ALEX.
DO YOU KNOW THE SOLUTION
TO THIS NUMBER TEN?

Alex says YEAH.

He says WHAT DO YOU DO?

Alex says YOU TAKE THE
EQUALS SIGN...
THE TOP ONE AND PUT IT
ON THE TOP OF THE MINUS.

He says RIGHT ON.
ONE EQUALS THREE MINUS TWO.
SUPER, ALEX.
WELL DONE.
NOW, LET'S SEE IF WE GOT
ANYBODY THAT KNOWS THE
SOLUTION TO THIS
ONE DOWN HERE.
IT'S GOT AN AWFUL
LOT OF STRAWS.
I DON'T KNOW IF I'M GOING TO
GET THEM ALL OUT THERE IN TIME
WHILE SOMEBODY'S PHONING IN.
THIS IS A NEAT ONE, TOO.
IT'S KIND OF LIKE
THE ONE ABOVE IT.
I MAY EVEN HAVE TO
DO THIS ON TWO LINES.
OKAY.
SO WE'RE MAKING A
CONNECTION, I THINK.
AND WE'RE JUST GETTING
THE PUZZLE OUT HERE,
WITH A LITTLE BIT OF LUCK.
LET'S SEE.
THAT'S IT.
AND WE'RE WORKING ON A
CONNECTION TO, I THINK,
JESSIE OR SAVANNAH FROM ELGIN.
WE'RE GOING TO HAVE
TO TRY SOMEBODY ELSE.
THE PHONE LINES...
YOU KNOW, MONDAY MORNING
BLUES WITH THE PHONE LINES.
LET'S SEE, WHO ARE
WE GOING TO GET?
HI, JENNIFER?

Jennifer says YEAH.

He says DO YOU KNOW HOW
TO SOLVE THIS ONE?

Jennifer says YEAH.

He says WHAT DO YOU DO?

Jennifer says OKAY, YOU MOVE...
SEE WHERE THERE'S,
LIKE, THREE?

He says YEAH.

Jennifer says AFTER THE PLUS SIGN,
YOU MOVE THAT ONE TO THE
END OF THE QUESTION.

He says THIS ONE?

Jennifer says YES.
NO, THE OTHER ONE.

He says SHOW ME.
THAT ONE?

Jennifer says OKAY.
YEAH, JUST MOVE IT TO, LIKE,
WHERE THE FOUR STICKS ARE
AND THEN...

He says ONE PLUS TWO PLUS
TWO EQUALS FIVE.

Jennifer says YEAH.

He says AND YOU'RE RIGHT.

Jennifer says OKAY.

He says ANYBODY KNOW
ANOTHER SOLUTION?
THERE'S ONE MORE SOLUTION,
BUT THAT WAS A GREAT ONE.

A schoolboy says HELLO?

He says HELLO.
HAVE YOU GOT A SOLUTION
TO THIS PROBLEM?

The schoolboy says YES.

He says WHAT DO YOU DO?

The schoolboy says YOU MOVE THE
ONE FROM THE TWO.

He says YEAH.

The schoolboy says AND YOU PUT
IT AT THE BOTTOM.

He says OKAY, SO THAT'S
GOING TO WORK AS WELL.
CAN I SHOW YOU ONE
MORE THAT'S GOING TO --
THAT DEFINITELY WORKS.
ONE PLUS ONE PLUS THREE.

The schoolboy says SURE.

He says BUT HERE'S ONE OTHER.
IT'S A LITTLE BIT TRICKIER.
IF I TAKE THAT ONE FROM THE
TWO AND MAKE ANOTHER PLUS
SIGN, ONE PLUS ONE PLUS ONE
PLUS ONE EQUALS FOUR, AND YOU
GUYS CAME UP WITH A COUPLE OF
REALLY GOOD ANSWERS AS WELL.
HERE'S THE ONE I WANT TO, OF
COURSE, THROW UP FOR THE LAST
ONE, MOVE NO STRAWS AT ALL
TO MAKE THE EQUATION TRUE.

He grabs a piece of paper that reads “12. Move no straws to make this equation true.” It shows an X, a plus, a I, an equal and an I and an X.

He continues AND TO BE QUITE HONEST, I'M
NOT GOING TO SET THE STRAWS OUT.
ANYBODY KNOW WHAT THE
SECRET OF THIS ONE IS?
MOVE NO STRAWS WHATSOEVER
TO MAKE THAT TRUE.
After a few moments, he continues AND HELLO, ERIC.

Eric says HELLO.

He says WHAT DO YOU DO?
HOW CAN I POSSIBLY SOLVE THIS
WITHOUT MOVING ANY STRAWS?

Eric says YOU CAN GO BACKWARDS.
NO, NOT UPSIDE DOWN.

He says BUT DOES...
I THOUGHT YOU MEANT...
WELL, BACKWARDS...
OH, I SEE WHAT YOU MEAN.
IT'S JUST...
READ IT THIS WAY?

Eric says AT THE BACK WHERE
IT SAYS, 'NINE',
LIKE ONE BEFORE...

He says YEAH.

Eric says YOU GO WITH THAT ONE,
PLUS ONE BESIDE ON THE LEFT.

He says RIGHT.

Eric says AND THEN THAT
EQUALS TEN.

He says THAT'S TRUE.
SO IN OTHER WORDS...
BUT YOU'RE MAKING A FLIP WITH
SOME STRAWS, BUT TAKE A LOOK.
WHEN I TURN IT UPSIDE
DOWN, ISN'T IT TRUE?
XI, WHICH IS ELEVEN, EQUALS
ONE PLUS TEN, RIGHT?

Eric says YEAH.

He says SO THAT'S HOW YOU DO IT
WITHOUT MOVING ANY STRAWS.
THANK YOU VERY MUCH
FOR CALLING IN.

Eric says OKAY.

He says NOW, I'VE GOT A QUICK
LITTLE LESSON THIS MORNING
THAT I'D LIKE TO GO THROUGH,
AND ONCE I'M DONE THE LESSON,
I'LL SEE IF I'VE GOT ENOUGH
TIME TO DO ONE MORE LITTLE
THING AND IT JUST DEPENDS.
THIS WEEKS' PROBLEM SET, YOU
HAVE TO DO AN INVESTIGATION
INVOLVING PERIMETER.
IT DOESN'T INVOLVE AREA, BUT
I THOUGHT I'D START WITH AREA
FIRST AND THEN COME
BACK TO PERIMETER.
VERY SIMPLE SITUATION.

He shows a blue piece of paper under the title “Rectangles and Pairs of Factors” that reads “a) 3 equals 3 times 1. b) 4 equals 4 times 1. 4 equals 2 times 2.” The paper shows a rectangle, a longer rectangle and a square.

He continues WHAT I'M INTERESTED IN HERE IS
THAT IF YOU TAKE ANY NUMBER
WHATSOEVER -- AND WE'RE LOOKING
AT WHOLE NUMBERS ONLY, NOT
FRACTIONS BUT WHOLE NUMBERS --
YOU CAN BREAK IT INTO PAIRS
OF FACTORS, MEANING, FOR
INSTANCE, THE NUMBER THREE,
THREE TIMES ONE.
WELL, THAT'S THE SAME AS A
RECTANGLE THAT HAS A WIDTH OF
ONE AND A LENGTH OF THREE.
SO THAT'S ONE WAY OF LOOKING
AT THE NUMBER THREE.
THE NUMBER FOUR, ON THE OTHER
HAND, CAN BE WRITTEN WITH TWO
SETS OF PAIRS OF FACTORS, FOUR
TIMES ONE AND TWO TIMES TWO.
SO THAT YOU CAN ACTUALLY
LOOK AT THAT NUMBER AS TWO
DIFFERENT RECTANGLES.
NOW, EVEN THOUGH THAT'S A
SQUARE, IT'S ALSO A RECTANGLE.
SO THERE'S A RELATIONSHIP
BETWEEN PAIRS OF FACTORS
AND RECTANGLES.
REMEMBER THAT, IN FACT,
THIS IS ABOUT AREA AS WELL,
SO THAT EACH ONE OF THESE,
THESE TWO HAS THE SAME AREA.
ONE TIMES FOUR IS FOUR,
TWO TIMES TWO IS FOUR.
IS THE PERIMETER THE
SAME IN EACH OF THESE?
WELL, IF YOU WERE TO DO
PERIMETER, WHICH IS THE
DISTANCE AROUND, IT'D BE
FOUR PLUS FOUR IS EIGHT PLUS,
PLUS ONE PLUS ONE IS TEN.
BUT THIS IS FOUR
TWOS; IT'S EIGHT.
SO NOTICE THAT EVEN THOUGH
THE AREA'S THE SAME,
THE PERIMETER IS DIFFERENT.
LET'S TAKE ONE MORE EXAMPLE.

He points to a new piece of paper that reads “c) 9 equals 9 times 1. 9 equals 3 times 3.” The paper shows a long rectangle and a square.

He continues NINE COULD BE WRITTEN AS NINE
TIMES ONE, A WIDTH OF ONE, A
LENGTH OF NINE, OR IT COULD BE
WRITTEN AS THREE TIMES THREE.
THE FACT IS I'VE GOT
ONE MORE EXAMPLE.
THE NUMBER TWELVE.

A sheet of paper reads “d) 12 equals 12 times 1. 12 equals 6 times 2. 12 equals 4 times 3.” The paper shows three different sized rectangles.

He continues EACH ONE OF THESE HAS THE
SAME AREA, BUT THE PERIMETERS
ALL CHANGE.
THE NUMBER TWELVE CAN BE
TWELVE TIMES ONE, SO ONE FOR
THE WIDTH AND TWELVE FOR
THE LENGTH, OR SIX BY TWO
OR FOUR BY THREE.
REMEMBER, WE'RE ONLY
WORKING WITH WHOLE NUMBERS.
NOW, I'M NOT GOING TO WRITE
THESE OUT BECAUSE ACTUALLY,
I THINK YOU FUNDAMENTALLY KNOW.

He takes another sheet of paper. It reads “Definitions. Perimeter. Area.”

He continues PERIMETER IS THE DISTANCE
AROUND AND AREA IS THE
AMOUNT OF SURFACE.

A new piece of paper under the title “Hold the Perimeter Constant” reads “Whole number side lengths. Try P equals 20.”

He continues YOUR PROBLEM THIS WEEK IS HOLD
THE PERIMETER CONSTANT INSTEAD
OF THE AREA AND LOOK AT THE
WHOLE NUMBER SIDE LENGTHS.
NOW, IF I HAVE SOMETHING THAT
HAS A PERIMETER OF TWENTY...
I'M GOING TO GET A
PIECE OF PAPER UP HERE.
YOU CAN HELP ME OUT.
IF I HAVE SOMETHING THAT
HAS A PERIMETER OF TWENTY,
WHAT CAN THE DIMENSIONS BE?
WHAT KINDS OF RECTANGLES
CAN I MAKE WITH A
PERIMETER OF TWENTY?

On a clean sheet of paper, he writes “P equals 20.”

He continues SO I'D LIKE YOU TO CALL IN
AND LET ME KNOW WHAT THE
POSSIBILITIES ARE, AND I'LL
JUST REALLY QUICKLY RECORD THEM.
I THINK WE'RE CONNECTING
TO SOMEBODY FROM ELGIN.
OKAY.
HELLO.
IS IT JESSIE OR SAVANNAH?

Jessie says HELLO?

He says HELLO.
IS IT JESSIE OR SAVANNAH?

Jessie says IT'S JESSIE.

He says OKAY.
CAN YOU GIVE ME AN EXAMPLE
OF A RECTANGLE THAT HAS A
PERIMETER OF TWENTY?

Jessie says TEN TIMES TEN.

He says TEN TIMES TEN?

Jessie says NO, TEN TIMES TWO.

He says THAT'S AN AREA OF
TWENTY, NOT A PERIMETER.

Jessie says OH, THANKS A LOT!
[laughing]

He says LET'S TRY
SOMEBODY ELSE.
I NEED A PERIMETER OF
TWENTY, NOT THE AREA.
REMEMBER, THIS IS A
LITTLE BIT DIFFERENT.

Hilary says HELLO?

He says HELLO.
HILARY OR JAYLENE?

Hilary says HILARY.

He says OKAY, HILARY, CAN YOU
GIVE ME AN EXAMPLE OF A
RECTANGLE THAT HAS A
PERIMETER OF TWENTY?

Hilary says YOU COULD DO,
LIKE, FOUR BY FIVE.

He says FOUR BY FIVE,
THAT'S AN AREA.
FOUR TIMES FIVE...
IS EQUAL TO TWENTY.
NOW, DOES THAT HAVE -- I'M
GOING TO DRAW THAT ONE.
THAT'S FOUR,
FIVE, FOUR, FIVE.
EIGHT PLUS TEN IS EIGHTEEN.
THE PERIMETER IS NOT TWENTY.
REMEMBER, IT'S THE PERIMETER
I WANT THAT'S TWENTY.

Hilary says OKAY.

He says OKAY, CAN I
HELP YOU OUT A BIT?

Hilary says OKAY.

He says AND THEN YOU GIVE
ME THE SECOND ONE.
IF I MAKE THAT ONE AND THAT
NINE, NOTICE THAT ONE PLUS
NINE IS TEN TIMES TWO IS...?

Hilary says TWENTY.

He says OKAY.
CAN YOU TRY ANOTHER
RECTANGLE THAT ALSO HAS
A PERIMETER OF TWENTY?
START WITH ANOTHER
NUMBER THERE.

Hilary says YOU COULD DO EIGHT...
TWO AND TWO AND
EIGHT AND EIGHT.

He says RIGHT ON.
GIVE ME ONE MORE, NOW
THAT YOU'VE GOT THE IDEA.

Hilary says YOU COULD DO SEVEN AND
SEVEN AND THREE AND THREE.

He says RIGHT.
SO YOU SEE, THIS
IS PRETTY EASY.
YOU WANT TO KEEP GOING?
YOU'RE ON A ROLL NOW.
TRY ANOTHER ONE.

He draws the rectangles and writes the numbers Hilary mentions.

Hilary says OKAY.
YOU COULD DO SIX AND FOUR.

He says YEAH.
ARE THERE ANY MORE?

Hilary says YOU COULD DO FIVE
AND FIVE AND FIVE.

He says RIGHT.
ARE THERE ANY MORE?

Hilary says NO.

He says NO, THERE AREN'T.
SO HOW MANY RECTANGLES DO
YOU GET WITH A PERIMETER
OF TWENTY?
REMEMBER, THE LENGTH AND THE
SIDES ARE WHOLE NUMBERS.

Hilary says YOU CAN GET FIVE.

He says THANK YOU VERY MUCH.
YOUR ASSIGNMENT THIS WEEK
ASKS YOU TO DO THAT EXACTLY.
THAT'S WHAT YOU'RE TRYING TO
DO, IS TO WORK OUT THE TOTAL
NUMBER OF RECTANGLES THAT
HAVE A CERTAIN PERIMETER, AND
WHAT WE JUST DID THERE IS A
REALLY GOOD EXAMPLE OF THAT.
[paper shuffling]
JUST CHECKING TO SEE IF
I'VE GOT ANYTHING ELSE HERE,
AND I DO.
WE HAVE THE HOLIDAY COMING UP,
AND SOMETIMES IT'S KIND OF
NEAT TO HAVE A LITTLE
PROBLEM TO DO.
NOW, YOU'VE GOT THAT LITTLE
ASSIGNMENT, BUT I'M GOING TO
LEAVE YOU ONE MORE PROBLEM
THAT'S KIND OF LIKE THE
MUFFIN PROBLEM I DID AT THE
BEGINNING, AND HERE IT IS.

A blue piece of paper under the title “A Holiday Challenge!” appears. It reads “Is it possible to cut a box into 27 individual cubes with less than 6 cuts? Why or why not?” The paper features a present and a 3-D cube.

He continues SO I'LL CALL IT THE HOLIDAY
CHALLENGE, AND THAT CAN MEAN
YOU GOT TO START THINKING
PERHAPS ABOUT GIFTS,
IF WE'RE LUCKY AT ALL.
SO THIS IS THE KIND OF
THING YOU'RE DEALING WITH.
YOU START WITH A CUBE, AND I
WANT TWENTY-SEVEN SMALL ONES.
NOW, REMEMBER THAT THIS CUBE
IS THREE BY THREE BY THREE
AND THREE TIMES THREE TIMES
THREE IS TWENTY-SEVEN.
SO THE QUESTION IS CAN I CUT
THIS IN SUCH A WAY THAT I CAN
USE LESS THAN SIX CUTS AND GET
TWENTY-SEVEN LITTLE PIECES?
SO THAT'S YOUR PROBLEM FOR
THE HOLIDAY, AND WHEN WE COME
BACK, I'M CERTAINLY GOING TO
WANT TO HEAR YOUR ANSWERS.
I GOT TO MAKE A MENTAL NOTE OF
THAT, THAT I WILL BE LOOKING
FOR YOUR ANSWERS IN JANUARY,
WHICH LONG TIME AWAY,
TO THIS LITTLE PROBLEM.
RIGHT NOW I WILL TAKE ANY
QUESTIONS YOU MIGHT HAVE ABOUT
THE ASSIGNMENT, AND WHILE WE
MAY BE CONNECTING TO SOMEBODY,
IS THERE ANYBODY PHONING IN?
YEAH, I THINK THERE IS.
WHILE WE'RE CONNECTING, WOULD
THE FACILITATOR AT ELGIN,
AFTER THE SHOW, CALL US
ON THE HELP LINE, PLEASE?
SO WE'RE GOING TO TAKE A CALL
AND SEE IF YOU HAVE A QUESTION
BEFORE WE SIGN OFF.

Sarah says HELLO?

He says HELLO, SARAH?

Sarah says YEAH.

He says HAVE YOU
GOT A QUESTION?

Sarah says YEAH.
DO WE HAVE TO WORK WITH OUR
PARTNERS IF WE HAVE ONE?

He says YOU MEAN FOR
THAT HOLIDAY CHALLENGE?

Sarah says YEAH.

He says NOPE.
YOU CAN DO THAT
ONE ON YOUR OWN.

Sarah says OKAY.

He says NO PROBLEM.

Sarah says BYE.

He says AND MAYBE WE CAN
TAKE ANOTHER CALL.
I SEE A FEW HERE.

Savannah says HELLO?

He says HELLO, JESSIE OR SAVANNAH?
JESSIE?

Savannah says SAVANNAH.

He says SAVANNAH, AH, GOOD.
WHAT'S YOUR QUESTION?

Savannah says CAN YOU DO IT
WITH SIX CUTS?

He says YES, YOU CAN
DO IT WITH SIX CUTS.
THE QUESTION IS, CAN
YOU DO IT WITH LESS?

Savannah says OKAY.

He says OKAY?

Savannah says THANKS.

He says SUPER.
AND WE'LL TAKE A
CALL FROM ELGIN.
NOW, WE MAY NOT BE ABLE TO
COVER EVERYBODY, BUT WE'LL
TRY TO GET A COUPLE
OF QUICK ONES.
HELLO.
IS IT TYLER OR CARRIE?

Tyler says HELLO?

He says HELLO, TYLER?

Tyler says YEAH.

He says OKAY, HAVE YOU
GOT A QUESTION?

Tyler says NO, NO.

He says OKAY, THANK YOU.
WE'LL TAKE ONE MORE CALL
BECAUSE WE'RE JUST ABOUT AT
THAT TIME WHEN WE
DO HAVE TO SIGN OFF.

Jennifer says HELLO?

He says HELLO, JENNIFER?

Jennifer says YEAH.

He says HAVE YOU
GOT A QUESTION?

Jennifer says YEAH.
DO WE GET TO FAX OUR STUFF IN
LIKE WE DID THAT ONE WEEK?

He says THAT'S A REALLY GREAT
IDEA, AND WHAT I'M GOING TO DO
IS, THE FACT IS, I'LL TELL YOU
WHAT I'M GOING TO DO RIGHT NOW.
I'M GOING TO PUT THE PHONE
NUMBER UP, THE FAX NUMBER.

Jennifer says OKAY.

He says SO THAT'S A
REALLY GOOD IDEA.

He writes “Fax (416) 484 2609. Mister C.”

He continues I'D LOVE TO HAVE YOUR
SOLUTIONS SENT IN TO ME.
AND ANYTHING THAT I GET THAT I
CAN PICK UP THAT MONDAY MORNING
BEFORE I COME ON
AIR, I'LL SHOW THEM.
THAT'S FANTASTIC.
ANYWAY, HAVE A GREAT,
GREAT HOLIDAY SEASON.
DO A LITTLE BIT OF RELAXING
AND, HOPEFULLY, LITTLE BIT OF
WINTER SPORTS, IF IT COMES
ALONG AT ONE OF THESE POINTS.
WE'LL SEE YOU IN THE NEW YEAR.
BYE-BYE.

The caption changes to “Please remember to log off! Pick up handset. Press number sign 7. Press 1 to confirm. Hang up handset. See you next time!”

Watch: Rectangles