Transcript: The Number | Mar 26, 1999

(music plays)

The opening slate pops up with a countdown timer from 20 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 black T-shirt with Einstein’s face and patterned suspenders.

Mister C says WELCOME TO THE VIRTUAL
CLASSROOM 1999.
IT'S MISTER C AGAIN, AND I'M
LOOKING FORWARD TO THE
NEW MILLENNIUM, A
MERE 361 DAYS AWAY.
TO GET US GOING IN THE NEW
YEAR, I'VE GOT A LITTLE BIT OF
A PUZZLE THAT I WANT YOU TO
TAKE A LITTLE BIT OF TIME
TO EVENTUALLY COPY DOWN.
I'M GOING TO
EXPLAIN IT TO YOU.
HERE IT IS.
WHAT WE HAVE IS A GRID THAT IS
SIX BY SIX, SO THERE ARE 36
SPOTS IN IT, AND MAYBE THE
VERY FIRST THING YOU DO IS YOU
FIND THESE SPOTS AND YOU BLANK
THEM OUT BECAUSE THEY REALLY
DON'T PLAY MUCH OF A ROLE.
WHAT YOU'RE ATTEMPTING TO
DO IS -- LET'S TAKE THIS
HORIZONTAL ROW UP AT
THE TOP, FOR INSTANCE.

A blue piece of paper shows a grid with the basic elementary arithmetic symbols scattered in the boxes. The first horizontal row equals 9, the third one equals 10 and the fifth one equals 31. The first vertical row equals 3, the third one equals 8 and the fifth one equals 2. Numbers 0 to 8 appear on small squares of paper.

He continues WE'RE USING THE DIGITS, ZERO,
ONE, TWO, THREE, FOUR, FIVE,
SIX, SEVEN AND EIGHT, SO THERE
ARE NINE OF THEM, TO FILL ONE,
TWO, THREE, FOUR, FIVE, SIX,
SEVEN, EIGHT, NINE SPOTS.
AH, BUT THE TRICK IS THIS --
THESE THREE NUMBERS HAVE TO
ADD TO NINE, AND IF WE'RE GOING
DOWN, THIS NUMBER TIMES THIS
NUMBER WILL GIVE A NUMBER,
DIVIDE THAT NUMBER BY THIS
ONE AND YOU SHOULD GET THREE.
SO THE NUMBERS AT THE BOTTOM
ARE WHAT HAPPENS VERTICALLY
AND THE NUMBERS AT THE SIDE
ARE WHAT HAPPENS HORIZONTALLY.
SO WHAT I'M GOING TO DO IS
I'M GOING TO MOVE THE DIGITS
ASIDE FOR A MOMENT OR TWO AND
WHAT I WANT TO DO IS GIVE YOU
ABOUT ONE MINUTE OR SO JUST TO
COPY IT DOWN, AND THEN I'LL
COME BACK ON AIR AND EXPLAIN
A LITTLE BIT MORE TO YOU AND
GIVE YOU A COUPLE OF MINUTES
THEN TO SOLVE IT ON YOUR OWN.
SO ONE MINUTE NOW JUST TO
COPY DOWN THAT GRAPHIC.
OKAY, NOW I'M GOING TO GO BACK
TO THE PUZZLE IN JUST A MOMENT
AND REMIND YOU ABOUT WHAT
YOU'RE ATTEMPTING TO DO AND
EXPLAIN A COUPLE OF THINGS YOU
MIGHT LOOK FOR TO HELP YOU
SOLVE THE PROBLEM, AND THEN
EVENTUALLY, I'LL GIVE YOU TWO
MINUTES TO GO AFTER IT.
NOW, HERE'S THE GRID ONE MORE
TIME, AND REMEMBER THAT WHAT
WE'RE TRYING TO DO IS WE'RE
TRYING TO PLACE NINE DIGITS,
INCLUDING A ZERO, UP TO EIGHT.
SO I'M JUST PUTTING THEM
AROUND THE EDGE AGAIN
TO REMIND YOU WHICH
DIGITS WE HAVE.
HOPEFULLY KEEP THEM STRAIGHT.
THAT IS A SIX, NOT A NINE.
OKAY.
NOW, THE IDEA IS, IS THAT
WE PLACE ALL THESE NINE IN,
IN EXACTLY ONE SPOT.
THESE THREE NUMBERS HERE
HAVE TO ADD TO NINE.
THIS NUMBER DIVIDED BY
THIS NUMBER TIMES THIS ONE
HAS TO EQUAL 10.
THIS ONE TIMES THIS ONE SUBTRACT
THIS ONE HAS TO EQUAL 31.
THAT LEADS ME TO BELIEVE
THAT THERE ARE SOME FAIRLY
LARGE NUMBERS GOING
ON THERE SOMEWHERE.
REASONABLY LARGE ANYWAY.
THIS NUMBER SUBTRACT THAT ONE
DIVIDED BY THIS ONE MUST GIVE
YOU A TWO.
NOW, REMEMBER, IT HAS TO BE
TWO EXACTLY, SO WHATEVER THESE
TWO NUMBERS ARE HAVE
TO END UP AS AN EVEN.
THIS NUMBER TIMES THIS ONE
PLUS THAT ONE EQUALS EIGHT.
WELL, THESE NUMBERS, SOMETHING
THERE CANNOT BE TERRIBLY
LARGE, ESPECIALLY IN
THE MULTIPLICATION.
THIS NUMBER TIMES THAT ONE
DIVIDED BY WHATEVER THIS IS
GIVES THREE.
NOW, I'M GOING TO SUGGEST THAT
MAYBE THE FIRST PLACE YOU
SHOULD BE LOOKING AT IS
PERHAPS THIS ROW RIGHT HERE
WITH THE 10.

He appears in a small window on the right bottom of the screen.

He continues TENS ARE PRETTY MAGICAL AND, TO
BE QUITE HONEST, THERE'S ONE
DIGIT THAT HAS TO GO IN THAT
ROW NO MATTER WHAT BECAUSE OF
THE DIVISION AND
THE MULTIPLICATION.
THERE'S ONE NUMBER THAT HAS TO
GO IN THAT ROW, AND THAT MIGHT
GET YOU STARTED.
SO REMEMBER THIS ROW HAS ONE
NUMBER IN PARTICULAR, AND WHAT
I WOULD LIKE TO DO NOW IS TO
GIVE YOU TWO MINUTES TO WORK
ON YOUR OWN AND SEE IF YOU CAN
COME UP WITH THE SOLUTION AND
THEN I'LL START TAKING PHONE
CALLS, AND WHAT WE'LL DO IS
WE'LL SORT OF SOLVE IT ONE
ROW OR A COLUMN AT A TIME.
EVENTUALLY, I'LL GIVE
YOU SOME EXTRA CLUES
AND WE'LL GO WITH THAT.
SO I'M GOING TO GIVE YOU,
STARTING NOW, TWO MINUTES
TO WORK ON THIS PUZZLE.

After a few minutes, he continues HELLO, I'M BACK.
NOW, I'M HOPING WITH A LITTLE
BIT OF LUCK YOU'VE HAD AN
OPPORTUNITY TO TRY TO BEGIN
TO FIGURE OUT THIS PUZZLE.
SO I'M GOING TO INVITE YOUR
PHONE CALLS RIGHT NOW TO MAYBE
HELP ME START THE PUZZLE
AND SEE WHAT HAPPENS.
WE GOT TO START
SOMEWHERE, SO EITHER --
I SEE WE HAVE A CALL COMING IN
FROM FLAMBOROUGH, BY THE LOOKS
OF IT, AND ONCE WE GET
CONNECTED THERE, THEN WE WILL
SEE IF WE CAN BEGIN
TO START THIS PUZZLE.
ONLY TAKE A MOMENT
OR TWO NOW.
HELLO.
WHO AM I SPEAKING TO?

He speaks with a spectator via a telephone conversation.

Josh says JOSH IN FLAMBOROUGH.

He says HI, JOSH.
YOU GOT LOTS OF
SNOW OUT THERE?

Josh says YEAH.

He says ARE YOU ENJOYING IT?

Josh says NO.

He laughs and says NO.
DID YOU HAVE TO
DO SOME SHOVELING?

Josh says YEAH.

He says YEAH, I COULD UNDERSTAND.
OKAY, WHERE WOULD YOU
LIKE ME TO START, JOSH?

Josh says PLACE THE THREE IN THE TOP
CORNER BY THE PLUS AND
THE TIMES SIGN.

He says RIGHT UP THERE, GOTCHA.

Josh says AND PLACE THE ONE UNDERNEATH
THE TIMES SIGN WHERE YOU PUT
THE THREE.

He says YES.

Josh says AND PUT THE ZERO
UNDERNEATH THE ONE.

He says OKAY.
NOW, I'M GOING TO
ASK YOU A QUESTION.
WHAT'S THREE DIVIDED BY ZERO?
HOW MANY ZEROS ARE
THERE IN THREE?

Josh says ZERO.

He says IT'S ONE OF THOSE ONES
YOU CAN'T DO BECAUSE
I DON'T KNOW THE ANSWER.
IT'S ONE OF THOSE
REALLY NASTY ONES.
I'LL REMIND YOU ABOUT
SOMETHING THAT, THERE'S A
RELATIONSHIP BETWEEN
DIVISION AND MULTIPLICATION.
NOW, LISTEN TO ME CAREFULLY
BECAUSE I DON'T HAVE A
SHEET UP HERE, BUT WHEN I
TAKE SIX DIVIDED BY TWO,
WHAT'S THE ANSWER?

Josh says THREE.

He says YEAH.
AND TO CHECK THE ANSWER, YOU
TAKE THE ANSWER THREE AND
MULTIPLY IT BY THE TWO, AND
THREE TIMES TWO EQUALS SIX,
DOESN'T IT?

Josh says YEAH.

He says OKAY.
NOW, THREE DIVIDED
BY ZERO EQUALS?

Josh says ZERO.

He says PICK A NUMBER, ANY
NUMBER YOU WANT.
SAY FIVE, WHAT THE HECK.
FIVE TIMES ZERO IS ZERO.
SO YOU SEE, WHAT HAPPENS THERE
IS NO MATTER WHAT YOU MULTIPLY
ZERO BY, WHAT DO
YOU ALWAYS GET?

Josh says ZERO.

He says SO YOU'RE NEVER GOING TO
GET THAT THREE, ARE YOU?

Josh says NO.

He says NOW, THAT'S A REALLY
IMPORTANT LESSON THAT YOU
CANNOT DIVIDE BY ZERO BECAUSE
NOT THE BEST MATHEMATICIAN
IN THE WORLD EVEN
KNOWS THE ANSWER.
FACT IS THE BEST MATHEMATICIAN
IN THE WORLD WILL SAY
THERE IS NO ANSWER, OKAY?

Josh says OKAY.

He says OKAY, SO THAT WAS A GOOD
TRY, BUT IT DOESN'T WORK.
SO I CAN'T DIVIDE BY ZERO.
LET'S GO TO ANOTHER CALL AND
SEE IF WE CAN MAKE ANOTHER
START HERE.
POUND NINE WILL DO THE TRICK.
COME ON, WE...
A COUPLE OF PLACES
WE COULD START.
I'M GOING TO REMIND YOU THAT
TO MAKE A 10 AND YOU HAVE TO
MULTIPLY, WHAT NUMBER
HERE IS A DEFINITE?
YOU GOT TO USE...
ONE OF THESE DIGITS HAS
DEFINITELY GOT TO BE USED.
I SEE WE HAVE A
CALL, SO THAT'S GOOD.
AND AGAIN, I DON'T SEE THE
NAMES TODAY SO I'M GOING TO
HAVE TO ASK YOU FOR YOUR
NAMES WHEN YOU CALL IN.
A MOMENT OR TWO WE SHOULD BE
CONNECTED TO FLAMBOROUGH,
I THINK.
HELLO.
WHO AM I SPEAKING TO NOW?

Phillip says PHILLIP.

He says HI, PHILLIP.
OKAY, NOW, WHERE DO
YOU WANT TO START?

Phillip says I WANT TO START WITH THE ZERO
BECAUSE IT CAN'T BE MULTIPLIED
OR DIVIDED BY WITHOUT SCREWING
THE ANSWER UP, SO IT HAS TO GO
BESIDE THE NINE.

He says OKAY, OKAY.
I'M MORE THAN WILLING
TO PUT IT THERE, YEAH.

Phillip says AND, ER... OH, I HAD IT.
I JUST FORGOT IT.

Mister C chuckles.

Phillip continues THE ONE GOES, I THINK
DOWN BY THE EIGHT.

He says DOWN BY THE EIGHT.
DOWN HERE?
IS THAT WHAT YOU MEAN?

Phillip says YUP, AND THEN
PUT THE EIGHT...

He says EIGHT?

Phillip says BESIDE IT, JUST
ABOVE THE TWO.

He says YEAH, YEAH.

Phillip says AND PUT...
OOPS, CAN YOU SWITCH
THE ONE AND THE EIGHT?

He says SURE, I CAN.

Phillip says AND THEN PUT THE FOUR IN THE
OTHER SQUARE IN THAT LINE.

He says OKAY.
FOUR TIMES EIGHT,
HEY, I LIKE IT.
THAT'S A GOOD ONE.
I LIKE THAT ROW.
THAT'S A...
AND I'M GOING TO TELL YOU
RIGHT NOW THAT THAT IS
A CORRECT ROW.
SO THAT'S A GOOD
STARTING POINT.
REALLY WELL DONE.
OKAY, LET'S TAKE ANOTHER CALL
AND SEE IF WE CAN GO A LITTLE
FURTHER THAN THIS.
WE HAVE ONE ROW IN THERE.
I'M GOING TO HAVE TO FOR
MY PIP TO BE ELIMINATED.
THERE WE GO.

Using a pen, he points to the fifth vertical row and says FOUR TIMES EIGHT
MINUS ONE IS 31.
THAT IS CORRECT.
I'M GOING TO SAY THAT THE
ZERO UP HERE IS NOT CORRECT,
SO I'M GOING TO
MOVE IT AWAY.
BUT THIS ROW RIGHT HERE
IS RIGHT ON THE BUZZER.
SO LET'S SEE, HAVE
WE GOT ANOTHER CALL?
WHO ARE WE SPEAKING TO NOW?

Thomas says THOMAS FROM FLAMBOROUGH.

He says HI, THOMAS.
HOW YOU DOING?

Thomas says FINE.

He says OKAY, WHAT DO YOU
WANT ME TO DO NEXT?

Thomas says WELL, TO GET THE EIGHT, I
THINK IT SHOULD BE ZERO...

He says YEAH.

Thomas says AT THE TOP.

He says YEAH.
OKAY, I LIKE THAT.
YOU'RE DEFINITELY RIGHT.
THAT ZERO HAS TO GO THERE.

Thomas says OKAY, TIMES TWO.

He says TIMES TWO.
OKAY, I'M GOING
TO PUT THAT THERE.

Thomas says TWO.
OH, WAIT.

He says WELL, THAT DOES WORK
FOR THIS ONE, I AGREE.

Thomas says YEAH.

He says OKAY.
I'M GOING TO ASK FOR SOMEBODY
TO CARRY ME FORWARD.
I'M GOING TO SAY RIGHT
NOW THAT THIS NUMBER IS
DEFINITELY CORRECT.
AND IS THERE ANOTHER CALL?
I WOULD LOVE TO HAVE SOME --
REMEMBER, THERE'S STILL ONE
DIGIT IN THIS ROW THAT HAS TO
BE THERE THAT I THINK WE COULD
PROBABLY DO SOMETHING WITH.
NO MORE CALLS?
ANYBODY FROM TRILLIUM?
OH, WE HAVE A CALL, SO I THINK
WE'LL TRY TO TAKE THIS ONE.
AND IT'S STILL FLAMBOROUGH.
AND FOR THOSE FOLKS THAT ARE
AT TRILLIUM, MORE THAN HAPPY
TO HEAR FROM YOU.

Phillip says HELLO?

He says OKAY, WHO AM I TALKING TO?

Phillip says PHILLIP, AGAIN.

He says OKAY, FAIR ENOUGH.
WHAT DO YOU THINK, PHILLIP?

Phillip says TRY THE SIX IN THE
TOP LEFT CORNER.

He says TOP LEFT, SIX.

Phillip says AND PUT THE THREE
BESIDE THE ZERO.

He says YUP.
Phillip says THAT DEFINITELY
WORKS GOING ACROSS.

He says THAT'S MY COMBINATION,
THE SIX, ZERO, THREE.

Phillip says YEAH, I...
THAT CAN WORK.
NOW WE GOT TO GET SOMETHING
TO WEDGE INTO THESE
TWO SPOTS HERE.
WE ONLY HAVE A SEVEN
AND A FIVE LEFT.
WHAT DO YOU THINK?
LET'S TAKE THIS ONE, FOR
EXAMPLE, OVER ON THIS SIDE.
NOW, CAN I PUT A SEVEN OR
A FIVE HERE AND GET A TWO?

Phillip says NO.

He says OKAY, SO THERE'S A PROBLEM
WITH THIS ONE RIGHT HERE,
ISN'T THERE?

Phillip says MM-HMM.
SWITCH THEM AROUND?

Phillip says WE COULD DO THAT.

Phillip says PUT THE FIVE UNDER AND PUT...

He says PUT THE FIVE UNDER.
YOU KNOW SOMETHING?
YOU'VE JUST GOT ONE
MORE CORRECT ONE.
THAT FIVE HAS TO GO THERE.
SIX MINUS FIVE IS ONLY 1.
IF THAT FIVE HAS TO BE THERE
AND THAT ONE HAS TO BE THERE,
WHAT NUMBER HAS TO GO HERE?

Phillip says SIX.

He says CHECK AGAIN.
SIX MINUS FIVE IS...?
ONE.
ONE DIVIDED BY ONE IS ONE.

Phillip says OH, SEVEN.

He says YEAH, RIGHT ON.
NOW, FIX IT UP FOR ME.
I'M GOING TO TELL YOU RIGHT
NOW THAT THIS IS CORRECT,
THAT, THAT, THAT,
THAT AND THAT.
OKAY, LET'S TAKE
ANOTHER ANSWER.
WE BASICALLY ARE
GETTING CLOSE.
I'M GOING TO TELL YOU THAT
THAT ONE'S INCORRECT.

He takes out number 2.

He continues SO ALL WE HAVE TO DO IS PLACE
THESE LAST THREE NUMBERS.
WHO AM I SPEAKING TO?

Sean says HELLO?

He says HELLO.
WHO IS IT?

Sean says SEAN.

He says HI, JOHN.
OKAY, WHAT DO I --
IS IT JOHN OR SEAN?

Sean says SEAN.

He says SORRY ABOUT THAT.
OKAY, WHERE DO I PUT THESE LAST
THREE NUMBERS SO THAT IT WORKS?
START WITH THIS ONE UP HERE.

Sean says THE TWO.

He says RIGHT ON.
NOTHING ELSE WILL
WORK, WILL IT?

Sean says NO.

He says OKAY.
THAT LEAVES ME WITH
THE SIX AND THE THREE.
WHERE DO THEY GO?
AND YOU ONLY HAVE
TWO SPOTS HERE NOW.
THINK CAREFULLY
BEFORE YOU ANSWER.

Sean says THE THREE UNDERNEATH THE TWO.

He says OKAY, LET'S CHECK IT OUT.
WHAT'S THREE TIMES TWO?

Sean says SIX.

He says DIVIDED BY FOUR?

Sean says ONE.

He says ONE PLUS A BIT, RIGHT?

Sean says MM-HMM.

He says SO THAT'S NOT IT,
IS IT?

Sean says NO.

He says WELL, LET'S TRY SIX.
SIX TIMES TWO?

Sean says TWELVE.

He says DIVIDED BY FOUR?

Sean says THREE.

He says HEY, THAT WORKS.
WELL, THAT'S...
AND YOU'RE HOPING
THAT THAT WORKS.
DOES IT WORK?

Sean says MM-HMM.

He says WELL DONE.
THANK YOU VERY MUCH.
SO THAT'S THE END OF THE
PUZZLE, AND I'M VERY PLEASED.

The first horizontal row reads “2 plus 0 plus 7 equals 9.,” the third horizontal row reads “6 divided by 3 multiplied by 5 equals 10” and the fifth horizontal row reads “4 multiplied by 8 minus 1 equals 31.” The first vertical row reads “2 multiplied by 6 divided by 4 equals 3,” the third vertical row reads “0 multiplied by 3 plus 8 equals 8” and the fifth vertical row reads “7 minus 5 divided by 1 equals 2.”

He continues IT'S NOT A SIMPLE PUZZLE, BUT I
MUST ADMIT THERE'S SOME PRETTY
IMPORTANT LITTLE MATH
IDEAS, SOME NUMERACY IDEAS.
WHEN YOU'RE TRYING TO MAKE A
10 AND YOU'RE MULTIPLYING,
YOU ALWAYS NEED A FIVE AND
YOU NEED AN EVEN NUMBER.
OBVIOUSLY A TWO IN THIS
PARTICULAR CASE.
THAT'S WHY I KEPT SAYING, IN
THAT PARTICULAR ROW WITH THE 10
THAT YOU KNOW THAT THE FIVE
HAD TO GO THERE SOMEWHERE.
THOSE ARE THE KINDS OF
THINGS THAT YOU HAVE TO
KEEP THINKING ABOUT.
THAT ISSUE THAT CAME UP AT THE
BEGINNING, DIVISION BY ZERO,
IT'S SOMETHING THAT YOU WILL
COME BACK TO YOU IN YOUR
MATH CLASSES IN GRADE SEVEN,
EIGHT AND SO ON FOREVER.
SOMEWHERE ALONG THE LINE,
SOMEBODY'S GOING TO SAY,
“WELL, YOU CAN'T
DIVIDE BY ZERO.”
YOU MUST UNDERSTAND AND THINK
ABOUT THAT IDEA THAT...
HOW MANY ZEROS ARE THERE
IN ANY WHOLE NUMBER?
YOU DON'T KNOW.
IT'S NOT POSSIBLE TO DO THAT.
SO THERE'S SOME PRETTY NEAT
IDEAS THAT CAME OUT OF THAT.
WHAT I WANT TO DO NOW IS GO
BACK TO YOUR HOMEWORK,
AND I'VE GOT A CHART HERE
THAT I'M GOING TO SHOW YOU
RIGHT AWAY.
IT'S THE RECTANGLE
SOLUTION CHART.

A blue piece of paper shows two columns. The first one reads “Perimeter. 4,6,8,10,12,14,16.” The second columns reads “Number rectangles.”

He continues AND FOR YOUR HOMEWORK THAT YOU
STARTED, OH, LONG TIME AGO,
THREE WEEKS AGO ANYWAY, YOU
WERE BASICALLY ASKED TO TELL
ME HOW MANY DIFFERENT
RECTANGLES YOU GET FOR
A CERTAIN PERIMETER.
LIKE, FOR INSTANCE,
THE PERIMETER OF FOUR.
NOW, REMEMBER THAT THE SIDES
HAVE TO BE WHOLE NUMBERS.
WHAT I'M GOING TO ASK YOU TO
DO IS I WILL ONLY ANSWER
THESE WITH YOUR PHONE CALLS.
SO YOU'VE GOT TO START PHONING
IN, AND IT'LL BE ONE PERSON TO
A SLOT AND YOU NEED
TO DO TWO THINGS.
ONE IS TO TELL ME HOW MANY
RECTANGLES; AND TWO IS TO TELL
ME WHAT THE DIMENSIONS
OF THOSE RECTANGLES ARE.
SO I CAN SEE SOME CALLS ARE
GETTING LINED UP, SO THAT'S
GOOD, AND WE'LL JUST
TAKE THEM RIGHT AWAY.
WHO AM I SPEAKING TO?

Jenny says IT'S JENNY FROM
FLAMBOROUGH CENTRE.

He says OKAY, JENNY FROM FLAMBOROUGH
CENTRE, HOW MANY RECTANGLES
PERIMETER FOUR?

Jenny says I GOT ONE RECTANGLE.

He says OKAY, AND WHAT ARE THE
DIMENSIONS OF THAT?

Jenny says THE LENGTH OF IT IS ONE UNIT
AND THE WIDTH OF IT IS ALSO
ONE UNIT.

He says VERY GOOD, JENNY.
THANK YOU VERY MUCH.
GOING TO THE NEXT CALL.
SO WE'RE...
HELLO AND WHO AM
I SPEAKING TO NOW?

Thomas says THOMAS.

He says HI, THOMAS.
PERIMETER SIX, HOW MANY?

Thomas says I GOT ONE RECTANGLE.

He says AND CAN YOU TELL ME
WHAT THE DIMENSIONS ARE?

Thomas says FOR LENGTH, IT'S TWO.

He says YEAH.

Thomas says AND FOR WIDTH, IT'S ONE.

He says WELL DONE.
THANK YOU VERY MUCH.
LET'S GO ON TO THE NEXT CALL.

He writes the answers he gets from the students.

Luke says THIS IS LUKE FROM
FLAMBOROUGH CENTRE.

He says PERIMETER EIGHT.
WHO AM I SPEAKING TO?

Thomas says LUKE.

He says HI, LUKE.
HOW MANY RECTANGLES,
PERIMETER EIGHT?

Thomas says TWO.

He says RIGHT ON.
WHAT ARE THE DIMENSIONS
OF THOSE TWO?

Thomas says ONE IS THREE AND ONE.

He says YEAH.

Thomas says AND THE OTHER IS THREE...
NO, IS TWO AND TWO.

He says EXCELLENT.
WELL DONE.
THANK YOU VERY MUCH.
OKAY, LET'S GO ON TO THE
NEXT CALL AND DO NUMBER 10.
WHO AM I SPEAKING TO?

Neil says THIS IS NEIL,
FLAMBOROUGH CENTRE.

He says OKAY, LET'S GO, NEIL.
WHAT DO YOU SAY?
HOW MANY?

Neil says JUST A SECOND, I NEED
TO LOOK AT MY PAPER.

He says THAT'S GOOD.
THAT'S WHAT I
WANT YOU TO DO.
[coughing]
EXCUSE ME.

Neil says THERE IS TWO WAYS.

He says YUP, AND CAN YOU TELL
ME THE DIMENSIONS?

Neil says THERE IS FOUR LENGTHS AND
FOUR WIDTH AND TWO LENGTHS
AND, AND THREE.
NO, AND THREE WIDTH.

He says YOU WERE FOUR AND ONE AND
TWO AND THREE, YOU'VE GOT IT.
YEAH, YOU DO HAVE IT, NEIL.
THANK YOU VERY MUCH.
LET'S GO TO THE NEXT
CALL FOR NUMBER 12.
HELLO.
WHO IS IT?

Jenny says IT'S JENNY FROM
FLAMBOROUGH CENTRE AGAIN.

He says OKAY, JENNY, HOW MANY?

Jenny says I GOT THREE.

He says AND CAN YOU TELL
ME THEIR DIMENSIONS?

Jenny says FIVE AND ONE.

He says YUP.

Jenny says FOUR AND TWO.

He says YUP.

Jenny says AND THREE AND THREE.
I MEAN, YEAH, THREE AND THREE.

He says THAT'S CORRECT.

Jenny says OKAY, THANKS.

He says THANK YOU VERY MUCH.
NEXT CALL.

He also draws the rectangles.

Nicole says HELLO?

He says AND, YES, WHO
AM I SPEAKING TO?

Jenny says NICOLE.

He says HI, NICOLE.
HOW MANY FOR 14?

Jenny says THERE WAS THREE
THAT I COULD FIND.

He says THAT'S GOOD, AND I WOULD
LIKE TO KNOW WHAT THEIR
DIMENSIONS ARE.

Jenny says THE LENGTH WAS SIX AND THE
WIDTH WAS ONE, AND THE LENGTH
WAS FIVE AND THE
WIDTH WAS TWO.

He says YUP.

Jenny says AND THE LENGTH WAS FOUR
AND THE WIDTH WAS THREE.

He says VERY GOOD.
YOU'RE DOING JUST GREAT.
ONE MORE CALL AND
WE FINISH THE CHART.

Ashton says HELLO.
IS THIS ROSE?

He says NO, IT'S ASHTON.

He says IT'S ASHTON, OKAY.
TELL ME HOW MANY FOR 16.

Ashton says FIVE.

He says FIVE.
NOW, TELL ME WHAT THEY ARE.

Ashton says FOUR.

He says FOUR.
YOU'RE GOING TO
CHANGE YOUR MIND.
YOU COULD TELL BY MY VOICE
THAT I WAS SURPRISED, RIGHT?

Ashton says YEAH.

He says OKAY, TELL ME WHAT THEY ARE.

Ashton says SEVEN AND ONE.
LENGTH.

He says YES, THAT'S FINE.

Ashton says SIX AND TWO.

He says RIGHT ON.

Ashton says FIVE AND THREE.

He says FIVE AND THREE, GOTCHA.

Ashton says AND FOUR AND FOUR.

He says EXCELLENT.
WELL DONE.

Ashton says THANK YOU.

He says NOW, WE'RE GOING TO DO
A LITTLE BIT OF A TEST,
SO TO SPEAK.
IT'S NOT SOMETHING THAT'S
GOING TO BE MARKED IN YOUR
MARKS BOOKS OR ANYTHING, BUT
I'M GOING TO GO THROUGH
FOUR QUESTIONS AND I WANT
EVERYBODY TO ANSWER.
AND WHAT I WILL DO IS
I'LL DO A QUESTION
AND SHOW YOU THE RESULT,
BUT I WON'T TELL YOU
FOR SURE WHETHER YOU'VE
GOT IT CORRECT OR NOT
UNTIL THE VERY END.
SO THERE ARE FOUR QUESTIONS,
AND I WANT YOU TO DO YOUR VERY
BEST TO GIVE ME AS GOOD...
AS MANY GOOD
ANSWERS AS POSSIBLE.
LET'S START WITH THIS ONE.
WHOOPS, WRONG THING.
WELL, WHERE ARE WE?
OH, WE GOT IT UP NOW.
SORRY ABOUT THAT.

A caption appears on screen under the title “Question Number 1.” It reads “How many distinct rectangles can be made with perimeter equals 18? 1: 3. 2: 4. 3: 6. 4: 8.” A gray bar graph reads “0 per cent.”

He continues NOW, I WANT TO SEE THESE
NUMBERS GO WAY, WAY, WAY UP.
EVERYBODY HAS TO ANSWER.
28 PERCENT,
OH, WE'RE GOING...
LET'S KEEP IT GOING.
EVERYBODY ANSWERS.
COME ON.
I WANT IT UP
OVER 80 PERCENT.
I SEE 72, 78.
ONE MORE PERSON.
EXCELLENT.

The bar graph changes to blue as numbers go up from “6 per cent” to “83 per cent.”

He continues LET'S TAKE A LOOK AT THAT.
OKAY.

A four-bar graph appears. A green bar reads “2,” a purple bar reads “10,” a blue bar reads “1” and a red bar reads “2.”

He continues WOULD YOU MAKE A NOTE THAT THE
VAST MAJORITY OF PEOPLE THINK
THAT THE CORRECT ANSWER FOR
THE FIRST QUESTION IS FOUR?
OKAY.
LET'S GO ON TO
THE NEXT QUESTION.

The caption changes to “Question Number 2.” It reads “How many distinct rectangles can be made with perimeter equals 24? 1: 3. 2: 4. 3: 6. 4: 8.” The gray bar graph reads “0 per cent.”

He continues NOW, I'M WATCHING THOSE
PERCENTAGES AGAIN,
AND THEY'RE GOING
UP PRETTY QUICKLY.
LET'S GO ALL THE WAY
TO 83 PERCENT ANYWAY.
ONE MORE PERSON,
ONE MORE PERSON.
HEY, WE'RE ALMOST THERE.
LET'S TAKE A LOOK AT IT.

The four-bar graph appears. The green bar reads “1,” the purple bar reads “0,” the blue bar reads “14” and the red bar reads “1.”

He continues NOW, WOULD YOU PLEASE MAKE A
NOTE THAT THE VAST MAJORITY,
I MEAN VAST MAJORITY, IN THIS
CASE THINK THAT THE CORRECT
ANSWER TO THAT QUESTION IS
SIX, AND LET'S GO ON TO
QUESTION NUMBER THREE.

The caption changes to “Question Number 3.” It reads “How many distinct rectangles can be made with perimeter equals 86? 1: 18. 2: 20. 3: 21. 4: 24.” The gray bar graph reads “0 per cent.”

He continues AGAIN, I'M WATCHING
THOSE PERCENTAGES.
GRAPH'S A LITTLE BIT
DIFFERENT THIS TIME.
LET'S SEE.
IT'S COMING.
ONE OR TWO MORE PEOPLE
AND I'LL BE HAPPY.
MAKE A COMMIT --
OKAY, FAIR ENOUGH.

The four-bar graph appears. The green bar reads “3,” the purple bar reads “3,” the blue bar reads “10” and the red bar reads “1.”

He continues THE MAJORITY OF PEOPLE, NOT
THE VAST MAJORITY THIS TIME,
BUT THE MAJORITY OF PEOPLE
FELT THAT THE CORRECT ANSWER
TO THAT QUESTION IS 21.
NOW, HERE'S THE ACID TEST.
THE LAST QUESTION HERE IS TO
REALLY TEST HOW YOU WENT ABOUT
FIGURING OUT HOW MANY
RECTANGLES FOR 86, BECAUSE I
DON'T THINK YOU PROBABLY
SAT DOWN AND DREW THEM ALL.
SO LET’S GO WITH QUESTION
NUMBER 4.

The caption changes to “Question Number 4.” It reads “What is the rule to determine the number of distinct rectangles with perimeter ‘n’, an even number? 1: 2/2. 2: 4n. 3: n/a and round down. 4: n/a and round up.” The gray bar graph reads “0 per cent.”

He continues AND N IS A NUMBER THAT
IS AN EVEN NUMBER.
DO YOU TAKE THE PERIMETER AND
DIVIDE IT BY TWO TO FIGURE OUT
HOW MANY RECTANGLES THERE ARE?
DO YOU TAKE THE PERIMETER AND
MULTIPLY IT BY FOUR TO FIGURE
OUT THE NUMBER OF RECTANGLES?
DO YOU TAKE THE PERIMETER AND
DIVIDE IT BY FOUR AND THEN
ROUND THE NUMBER DOWN, IF
NECESSARY, TO GET THE NUMBER
OF RECTANGLES?
OR DO YOU THINK YOU TAKE
THE PERIMETER N, DIVIDE IT
BY FOUR AND ROUND UP?
THIS IS THE TOUGH QUESTION, AND
I'M GOING TO WAIT UNTIL WE GET
A WHOLE BUNCH OF PEOPLE
ANSWERING THIS ONE.
WE ONLY HAVE A FEW OF YOU, SO
I'M NOT PREPARED TO SHOW YOU
THE ANSWERS YET.
I WANT TO BE OVER 80 PERCENT.
I WILL NOT BUDGE UNTIL
I'M OVER 80 PERCENT.
COUPLE MORE PEOPLE
AND THEN WE'RE THERE.
OKAY, WE'RE OVER 80 PERCENT.

The bar graph changes to blue as numbers go up from “6 per cent” to “83 per cent.”

He continues LET'S TAKE A LOOK
AT THE RESULT.
THIS IS INTERESTING.

The four-bar graph appears. The green bar reads “5,” the purple bar reads “0,” the blue bar reads “4” and the red bar reads “7.”

He continues THE RESULT, FIRST OF ALL, I
WON'T CALL IT A DEAD HEAT,
BUT WE HAVE THREE DIFFERENT
ANSWERS THAT COULD BE SEEN
TO BE POSSIBLE.
SO LET'S CHECK IT OUT.
I THINK WE'D BETTER
CHECK IT OUT.
LET'S GO TO...
BACK TO THE GRAPHICS CAMERA.

He shows the Rectangle Solution Chart.

He continues WHAT WE'RE LOOKING AT IS THE
RELATIONSHIP BETWEEN THIS
NUMBER HERE AND
THIS NUMBER HERE.

He points to the first row that reads “Perimeter 4” and “Numbers rectangles: 1.”

He continues NOW SOME PEOPLE SAID THAT THE
CORRECT ANSWER IN THE LAST
QUESTION WAS N, WHICH IS
LIKE THIS NUMBER HERE,
DIVIDED BY TWO.
IS FOUR DIVIDED BY
TWO EQUAL TO ONE?
NO.
SO IT'S NOT QUITE
THAT, IS IT?
BUT FOUR DIVIDED BY FOUR
DEFINITELY EQUALS ONE.
NOW, I WANT YOU TO LOOK AT
THIS ONE, THIS ONE, THIS ONE...
I WANT YOU JUST TO
LOOK AT THOSE NUMBERS.
CONTROL ROOM, IS IT POSSIBLE
TO CLEAR OFF THE ANSWERS TO
THAT LAST QUESTION
AND RE-RUN IT?
WHAT I'M GOING TO DO IS I WANT
YOU TO LOOK AT THOSE NUMBERS
FOR A FEW SECONDS, AND I'M
GOING TO ASK THE FOURTH
QUESTION ONE MORE TIME,
NOW THAT YOU'VE SEEN
THOSE QUESTIONS.
SO IT'LL TAKE A MOMENT OR TWO
TO GET SET UP AND GIVE YOU
AMPLE TIME TO LOOK AT THE
RELATIONSHIP BETWEEN THIS
NUMBER AND THIS, THIS AND
THIS, THIS AND THIS,
THIS AND THIS, AND SO ON.
JUST LOOK AT THOSE NUMBERS.
I THINK WE'RE PRETTY MUCH
READY TO TRY THE QUESTION AGAIN.
THERE IT IS.
OKAY.
IT'S THE SAME THING.
I WANT YOU TO ANSWER
THIS QUESTION AGAIN.
NOW, THINK ABOUT IT.
33 PERCENT.
I WANT EVERYBODY TO ANSWER.
YOU'VE HAD A CHANCE TO LOOK
AT THOSE NUMBERS AGAIN.

The bar graph changes to blue as numbers go up from “6 per cent” to “89 per cent.”

He continues OKAY, LET'S TAKE A LOOK.

The four-bar graph appears. The green bar reads “0,” the purple bar reads “0,” the blue bar reads “5” and the red bar reads “11.”

He continues THIS IS ONE OF THESE
SITUATIONS WHERE I'M AFRAID TO
SAY MAJORITY IS NOT CORRECT.
YOU DID ELIMINATE N DIVIDED BY
TWO, BUT LET'S TAKE A LOOK.
IF I DIVIDE THIS
BY 4, I GET 1.5,
BUT THE ANSWER'S ONE.

On the rectangle solution chart, he points to number 6 and “divided by 4 equals 1.5.”

He continues DO I ROUND DOWN OR ROUND UP?
IF I DIVIDE THIS
BY 4, I GET 2.
WELL, THAT'S RIGHT ON
SO THERE'S NO PROBLEM.
IF I DIVIDE THIS
BY 4, I GET 2.5.
DO I ROUND UP
OR ROUND DOWN?
IT'S A 2, SO IT'S LESS THAN
THIS; IT'S A ROUND DOWN.
SO THE CORRECT SOLUTION IS
IT'S N DIVIDED BY 4
AND ROUND DOWN.
IT'S REALLY IMPORTANT TO LOOK
VERY CAREFULLY AT HOW THE
NUMBERS WORK.
YOU HAD THEM ALL...
Pointing to the “Numbers rectangles” column, he continues YOU HAD ALL OF THESE CORRECT.
SO TRYING TO IDENTIFY THE
RULE IS THE NEXT TRICK.
IT'S A GOOD LESSON AND I THINK
THAT, FOR THE MOST PART, YOU
GUYS TRIED REALLY HARD AND I
THINK YOU CERTAINLY DID THE
EXERCISE WELL.
WHEN IT CAME TO THIS, IT
WAS A LITTLE BIT OF A TRICK.
THAT'S OKAY.
NOW, WHAT I WOULD LIKE TO DO
IS TO JUST, FIRST OF ALL,
REMIND YOU... OR
TELL YOU OR REVIEW.
I'M NOT EVEN GOING TO
DO MUCH OF A REVIEW.
THE EXERCISE COMING UP FOR
THIS WEEK IS SOMETHING SIMILAR
TO WHAT YOU'VE DONE ALREADY.
FACT IS IT INVOLVES ALL OF THE
THINGS THAT YOU DID WITH THE
DANCING EXERCISE.
SO WHAT I'M GOING TO ASK YOU
TO DO IS TO PHONE IN RIGHT NOW
AND YOU TELL ME WHAT
MATHEMATICS WE WERE STUDYING
WHEN WE DID THE
DANCING EXERCISE.
GIVE ME A CALL AND TELL ME
WHAT WE WERE DOING, BECAUSE
THAT'S EXACTLY WHAT
YOU'LL BE DOING FOR
THE WEEK COMING UP
IN THIS NEXT EXERCISE.
AND I SEE WE DO HAVE A CALL.
SO THE MOMENT THAT GETS
CONNECTED, WE'LL FIND OUT HOW
GOOD YOUR MEMORIES ARE.
JUST A MOMENT HERE.
HELLO, WHO AM
I SPEAKING TO?

Josh says JOSH.

He says HI, JOSH.
DO YOU REMEMBER WHAT WE WERE
DOING IN THAT SECOND ONE
WITH THE DANCING?

Josh says WE WERE DOING THE
TURNS AND FLIPS.

He says TURNS, FLIPS AND...?
WHAT'S THE OTHER ONE?

Josh says SLIDES.

He says OKAY.
NOW, I'M GOING TO...
I'M GOING TO OPEN THE
PHONE LINES ONE MORE TIME.
TURNS, FLIPS AND SLIDES.
WHAT'S THE MORE FORMAL
WAY TO SAY THAT?
IN OTHER WORDS, THERE ARE
OTHER WORDS THAT MEAN THE SAME.
THERE ARE...
SO I'M GOING TO ASK SOMEBODY
TO PHONE IN AND TELL ME WHAT
THE OTHER TERMS ARE
FOR THE SAME THING.
CERTAINLY, THAT ANSWER WAS
CORRECT AND I'M QUITE HAPPY
WITH THAT.
OKAY, WHO AM I SPEAKING TO?

Jen says IT'S JEN FROM
FLAMBOROUGH CENTRE AGAIN.

He says OKAY.
WHAT DO YOU CALL FLIPS, TURNS
AND SLIDES, ANOTHER WAY OF
SAYING IT?

Jen says THE OTHER WAY OF SAYING
THEM IS TRANSLATIONS.

He says WHICH ONE IS THAT?

Jen says I THINK THAT'S A SLIDE.

He says RIGHT ON.
TRANSLATIONS ARE SLIDES.

Jen says AND REFLECTIONS...

He says ARE?

Jen says ARE FLIPS.

He says RIGHT ON.

Jen says A TURN IS A ROTATION.

He says FANTASTIC!
SO THAT'S WHAT YOU'RE GOING TO
BE DOING WITH THIS EXERCISE
COMING UP THIS WEEK, EXCEPT
THAT I'M DOING IT BACKWARDS.
I'M GOING TO GIVE YOU
INSTRUCTIONS ABOUT HOW TO MOVE
A WHOLE BUNCH OF DIFFERENT
OBJECT, AND YOU'RE SUPPOSED
TO SEE SOMETHING THAT
COMES OUT OF THAT.
OKAY.
NOW, I'M GOING TO...
I'M GOING TO SHOW YOU THE SECOND
QUESTION ON YOUR EXERCISE.
YOU DON'T HAVE TO READ THIS
BECAUSE IT'S FULLY TYPED OUT.
IT'S EXACTLY VERBATIM WHAT YOU
HAVE ON YOUR EXERCISE SHEET.
WHAT IT SAYS IS:

He grabs a new sheet of paper that reads “2. Choose a numeral from 3 to 9. Draw a large, bold version of it on graph paper. Cut it out and then cut that numeral into four pieces. Paste these pieces on another piece of grid paper so that it is possible to ‘reconstruct’ the original using commands similar to those above. Write out your commands but you must keep in mind that you must use at least two translations (one horizontal and one vertical), two reflections (one horizontal and one vertical), and one rotation about the centre of your grid.

He continues THERE'S ONLY ONE REASON WHY
I WANTED TO SHOW YOU THIS.
THERE'S NO CHANGE
HERE, BUT I DO...
I WOULD LOVE TO SEE SOME OF
YOUR SOLUTIONS FAXED IN TO ME,
AND HERE'S HOW YOU DO IT.
FAX YOUR SOLUTIONS TO ME,
PREFERABLY BEFORE FRIDAY,
WELL, IT'LL HAVE TO
BE BEFORE FRIDAY, AT:

He shows a piece of paper that reads “Fax your solutions to Mister C at (416) 484 2609.”

He continues SO YOU WILL HAVE
TO DO A SIMILAR...
CREATE A SIMILAR PROBLEM TO
WHAT I GAVE YOU AND WHAT I'D
LIKE YOU TO DO IS TO PUT IT
ALL ON A PIECE OF PAPER WITH
YOUR INSTRUCTIONS AND
SO ON AND SO FORTH.
FAX IT TO ME AND I'LL SHOW AS
MANY SOLUTIONS AS POSSIBLE
ON AIR, AND I WOULD LOVE TO DO
THAT SO I'M LOOKING FORWARD
TO THAT.
NOW, SINCE IT IS THE
MILLENNIUM, OR NEAR THE
MILLENNIUM OR APPROACHING
THE MILLENNIUM, I THOUGHT...
AND IT'S A NEW YEAR.
I THOUGHT I MIGHT LEAVE YOU
WITH ONE MORE LITTLE PROBLEM
TO DO OVER THE
COURSE OF NEXT WEEK.
THIS IS JUST A LITTLE PUZZLE,
AND HERE'S HOW THE PUZZLE GOES:
IT'S CALLED THE FEWEST MOVES.

A blue piece of paper under the title “The Fewest Moves” appears. It reads “Horizontal, vertical or diagonal to reverse the positions of the pennies and the nickels.” The paper shows 2 rows of 3 boxes. Two boxes read “P “ and other two read “N.”

He continues AND I SUGGEST PENNIES AND
NICKELS BUT...
[coins clinking]
I'VE GOT QUARTERS AND
TOONIES, WHICH WILL DO
FOR THE TIME BEING.

He places 4 coins on the boxes with the letters.

He continues THE IDEA HERE IS THAT WE WANT
TO KNOW THE FEWEST NUMBER OF
MOVES THAT IT WOULD TAKE TO
SWITCH THE POSITION OF THE
QUARTERS AND THE TOONIES.
IN OTHER WORDS, THAT'S
THE FINAL POSITION.
I'LL SHOW YOU ONE MORE TIME.
I WANT TO KNOW THE FEWEST
NUMBER OF MOVES SO THAT THESE
TWO TOONIES END UP HERE AND
THESE TWO QUARTERS END UP HERE.

He moves 2 of the coins down and the others 2 up.

He continues NOW, WHAT KINDS OF MOVES ARE
YOU ALLOWED TO MAKE AND HOW DO
YOU COUNT THEM?
WELL, YOU CAN MAKE A
HORIZONTAL MOVE LIKE THAT.
THAT'D BE ONE MOVE.
THAT'D BE ANOTHER MOVE,
EVERY TIME YOU MOVE IT.
DIAGONAL MOVES, YOU'RE
ALLOWED TO DO THIS,
SO THIS WOULD BE A MOVE.
AS LONG AS THE SPACE IS
OPEN, YOU CAN MOVE IT THERE.
VERTICAL MOVE, THERE'S
A MOVE LIKE THAT.
SO WHAT I'M ASKING YOU IS THE
FEWEST NUMBER OF MOVES TO GET
THESE QUARTERS INTERCHANGED
WITH THOSE TOONIES.
THAT'S A REALLY NICE PROBLEM
FROM THE POINT OF VIEW THAT IT
KIND OF FITS WITH THE
EXERCISE YOU'RE DOING.
IT HAS TO DO WITH PERHAPS
TRANSLATIONS, AND YOU MIGHT
EVEN LOOK AT IT AS
PERHAPS EVEN REFLECTIONS.
SO THAT'S THE PROBLEM I'M
GOING TO LEAVE YOU WITH.
NOW, IF YOU'VE GOT ANY
QUESTIONS WHATSOEVER,
I'D BE MORE THAN HAPPY
TO ANSWER THEM FOR YOU.
AND I SEE WE DO HAVE A CALL.
HELLO, WHO AM I SPEAKING TO?

Luke says LUKE.

He says HI, LUKE.

Luke says FLAMBOROUGH CENTRE.

He says YEAH.
WHAT'S YOUR QUESTION?

Luke says I WAS WONDERING WHY THREE BY
TWO IS NOT CONSIDERED TO BE
A DISTINCT TRIANGLE,
I MEAN RECTANGLE?

He says OH, IN OTHER WORDS, IT'S
THE DIFFERENCE BETWEEN...
AND CAN I JUST USE A PIECE OF
PAPER HERE AND TRY TO EXPLAIN
IT TO YOU?
[coins clinking]
I'LL MOVE MY
QUARTERS AND SO ON.
[paper shuffling]
NOW, MY DRAWING, OBVIOUSLY,
IS VERY, VERY ROUGH.
THAT'S TWO, THAT'S THREE,
THAT'S TWO, THAT'S THREE.
NOW, FIRST OF ALL, THESE
TWO RECTANGLES ARE
EXACTLY CONGRUENT.
WHAT DO I MEAN BY CONGRUENT?
YOU'RE STILL ON
THE PHONE, RIGHT?

Luke says YEAH.
THE SAME?

He says THEY'RE EXACTLY THE SAME
IN SHAPE AND SIZE, RIGHT?

Luke says RIGHT.

He says AND THAT'S THE REASON I'M NOT
COUNTING BOTH OF THEM, BECAUSE
THIS IS THE SAME SHAPE
AND SIZE AS THIS ONE.
THE ONLY DIFFERENCE IS - AND
THIS IS THE WORD WE USE IN
MATHEMATICS -- 'ORIENTATION'.

He writes reads “orientation” and continues
IN OTHER WORDS, THIS IS
ORIENTED HORIZONTALLY.
THIS IS ORIENTED VERTICALLY.
SO BECAUSE OF THAT, I DON'T
WANT TO COUNT THEM TWICE.
THIS IS ONE RECTANGLE
AND ONCE I'VE GOT THAT ONE,
I REALLY HAVE THAT ONE, TOO.
IS THAT OKAY?

Luke says YEAH.
OKAY, THANKS.
BYE.

He says ANY OTHER QUESTIONS?
ANYWAY, IT'S BEEN A PLEASURE
BEING BACK IN 1999.
I HOPE THAT YOU HAVE LOTS OF
SUCCESS, AND I HOPE THAT YOU
CAN DIG YOUR WAY OUT OF
THIS TERRIBLE SNOWSTORM
AND HAVE SOME TIME TO
HAVE SOME FUN IN THE SNOW.
WE'LL SEE YOU SAME TIME,
SAME PLACE NEXT WEEK.
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: The Number